Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-26T18:32:20.965Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  19 December 2022

Pertti Mattila
Affiliation:
University of Helsinki
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Rectifiability
A Survey
, pp. 149 - 170
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlfors, L. V., Bounded analytic functions, Duke Math. J. 14 (1947), 111.Google Scholar
Alberti, G., Rank one property for derivatives of functions with bounded variation, Proc. R. Soc. Edinburgh Sect. A 123 (1993), 239274.Google Scholar
Alberti, G., Csörnyei, M. and Preiss, D., Structure of null sets in the plane and applications, In European Congress of Mathematics, 322, Eur. Math. Soc., 2005.Google Scholar
Alberti, G., Csörnyei, M. and Preiss, D., Differentiability of Lipschitz functions, structure of null sets, and other problems, In Proceedings of the International Congress of Mathematicians, Volume III, 13791394, Hindustan Book Agency, 2010.Google Scholar
Alberti, G. and Marchese, D., On the differentiability of Lipschitz functions with respect to measures in the Euclidean space, Geom. Funct. Anal. 26 (2016), 166.Google Scholar
Aliaga, R. J., Gartland, C., Petitjean, C. and Procházka, A., Purely 1-unrectifiable spaces and locally flat Lipschitz functions, arXiv:2103.09370.Google Scholar
Allard, W., On the first variation of a varifold, Ann. of Math. 95 (1972), 418446.Google Scholar
Almgren Jr., F. J., Plateau’s Problem, W. A. Benjamin, 1966.Google Scholar
Almgren Jr., F. J., Existence and Regularity Almost Everywhere of Solutions to Elliptic Variational Problems with Constraints, Mem. Amer. Math. Soc. 4, American Mathematical Society, 1976.Google Scholar
Almgren Jr., F. J., Almgren’s Big Regularity Paper, World Scientific Monograph Series in Mathematics 1, World Scientific Publishing, 2000.Google Scholar
Alper, O., Rectifiability of line defects in liquid crystals with variable degree of orientation, Arch. Ration. Mech. Anal. 228 (2018), 309339.Google Scholar
Alper, O., On the singular set of free interface in an optimal partition problem, Comm. Pure Appl. Math. 73 (2020), 855915.Google Scholar
Ambrosio, L., Metric space valued functions of bounded variation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1990), 439478.Google Scholar
Ambrosio, L., Coscia, A. and Dal Maso, G., Fine properties of functions with bounded deformation, Arch. Ration. Mech. Anal. 139 (1997), 201238.Google Scholar
Ambrosio, L., Fusco, G. and Pallara, D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, 2000.Google Scholar
Ambrosio, L. and Kirchheim, B., Rectifiable sets in metric and Banach spaces, Math. Ann. 318 (2000), 527555.Google Scholar
Ambrosio, L. and Kirchheim, B., Currents in metric spaces, Acta Math. 185 (2000), 180.Google Scholar
Ambrosio, L., Kirchheim, B. and Lecumberry, M., On the rectifiability of defect measures arising in a micromagnetics model, Nonlinear problems in mathematical physics and related topics, II, 2960, Int. Math. Ser. (N.Y.), 2, Kluwer/Plenum, 2002.Google Scholar
Ambrosio, L., Kleiner, B. and Le Donne, E., Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane, J. Geom. Anal. 19 (2009), 509540.Google Scholar
Ambrosio, L. and Soner, H. M., A measure-theoretic approach to higher codimension mean curvature flows, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997), 2749.Google Scholar
Antonelli, G., Brena, C. and Pasqualetto, E., On rectifiable measures in Carnot groups: existence of density, arXiv:2204.04921.Google Scholar
Antonelli, G. and Le Donne, E., Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces, Nonlinear Anal. 200 (2020), 111983.Google Scholar
Antonelli, G. and Merlo, A., On rectifiable measures in Carnot groups: existence of density, arXiv:2009.13941.Google Scholar
Antonelli, G. and Merlo, A., On rectifiable measures in Carnot groups: representation, Calc. Var. Partial Differential Equations 61 (2022), 52 pp.Google Scholar
Antonelli, G. and Merlo, A., On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion, J. Funct. Anal. 283 (2022), Paper No. 109495.Google Scholar
Anzellotti, G. and Serapioni, R., Ck rectifiable sets, J. Reine Angew. Math. 453 (1994), 120.Google Scholar
Arena, L. and Serapioni, R., Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs, Calc. Var. Partial Differential Equations 35 (2009), 517536.Google Scholar
Armitage, D. H. and Gardiner, S. J., Classical Potential Theory, Springer-Verlag, 2001.Google Scholar
Arroyo-Rabasa, A., Philippis, G. De, Hirsch, J. and Rindler, F., Dimensional estimates and rectifiability for measures satisfying linear PDE constraints, Geom. Funct. Anal. 29 (2019), 639658.Google Scholar
Azzam, J., Poincaré inequalities and uniform rectifiability, Rev. Mat. Iberoam. 37 (2021), 21612190.Google Scholar
Azzam, J., Semi-uniform domains and the A property for harmonic measure, Int. Math. Res. Not. IMRN (2021), 67176771.Google Scholar
Azzam, J. and Dabrowski, D., An α-number characterization of Lp spaces on uniformly rectifiable sets, arXiv:2009.10111.Google Scholar
Azzam, J., David, G. and Toro, T., Wasserstein distance and the rectifiability of doubling measures: Part I, Math. Ann. 364 (2016), 151224.Google Scholar
Azzam, J., David, G. and Toro, T., Wasserstein distance and the rectifiability of doubling measures: part II, Math. Z. 286 (2017), 861891.Google Scholar
Azzam, J., Hofmann, S., Martell, J. M., Mayboroda, S., Mourgoglou, M., Tolsa, X. and Volberg, A., Rectifiability of harmonic measure, Geom. Funct. Anal. 26 (2016), 703728.Google Scholar
Azzam, J., Hofmann, S., Martell, J. M., Mourgoglou, M. and Tolsa, X., Harmonic measure and quantitative connectivity: geometric characterization of the Lpsolvability of the Dirichlet problem, Invent. Math. 222 (2020), 881993.Google Scholar
Azzam, J. and Hyde, M., The weak lower density condition and uniform rectifiability, arXiv:2005.02030.Google Scholar
Azzam, J., Mourgoglou, M. and Tolsa, X., A two-phase free boundary problem for harmonic measure and uniform rectifiability, Comm. Pure. Appl. Math. 70 (2017), 21212163.Google Scholar
Azzam, J., Mourgoglou, M., Tolsa, X. and Volberg, A., On a two-phase problem for harmonic measure in general domains, Amer. J. Math. 141 (2019), 12591279.Google Scholar
Azzam, J. and Schul, R., Hard Sard: quantitative implicit function and extension theorem for Lipschitz maps, Geom. Funct. Anal. 22 (2012), 10621123.Google Scholar
Azzam, J. and Schul, R., An analyst’s traveling salesman theorem for sets of dimension larger than one, Math. Ann. 370 (2018), 13891476.Google Scholar
Azzam, J. and Tolsa, X., Characterization of n-rectifiability in terms of Jones’ square function: Part II, Geom. Funct. Anal. 25 (2015), 13711412.Google Scholar
Azzam, J., Tolsa, X. and Toro, T., Characterization of rectifiable measures in terms of α-numbers, Trans. Amer. Math. Soc. 373 (2020), 79918037.Google Scholar
Azzam, J. and Villa, M., Quantitative comparisons of multiscale geometric properties, Anal. PDE 14 (2021), 18731904.Google Scholar
Badger, M., Generalized rectifiability of measures and the identification problem, Complex Anal. Synerg. 5 (2019), Paper No. 2, 17 pp. Correction ibid Paper No. 11.Google Scholar
Badger, M., Li, S. and Zimmerman, S., Identifying 1-rectifiable measures in Carnot groups, arXiv:2109.06753.Google Scholar
Badger, M. and Naples, L., Radon measures and Lipschitz graphs, Bull. Lond. Math. Soc. 53 (2021), 921936.Google Scholar
Badger, M., Naples, L. and Vellis, V., Hölder curves and parameterizations in the analyst’s traveling salesman theorem, Adv. Math. 349 (2019), 564647.Google Scholar
Badger, M. and Schul, R., Multiscale analysis of 1-rectiable measures: necessary conditions, Math. Ann. 361 (2015), 10551074.Google Scholar
Badger, M. and Schul, R., Two sufficient conditions for rectifiable measures, Proc. Amer. Math. Soc. 144 (2016), 24452454.Google Scholar
Badger, M. and Schul, R., Multiscale analysis of 1-rectifiable measures II: characterizations, Anal. Geom. Metr. Spaces 5 (2017), 139.Google Scholar
Badger, M. and Vellis, V., Geometry of measures in real dimensions via Hölder parameterizations, J. Geom. Anal. 29 (2019), 11531192.Google Scholar
Balogh, Z., Size of characteristic sets and functions with prescribed gradient, J. Reine Angew. Math. 564 (2003), 6383.Google Scholar
Balogh, Z., Fässler, K., Mattila, P. and Tyson, J. T., Projection and slicing theorems in Heisenberg groups, Adv. Math. 231 (2012), 569604.Google Scholar
Balogh, Z., T. Tyson, J. and Warhurst, B., Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups, Adv. Math. 220 (2009), no. 2, 560619.Google Scholar
Bate, D., Structure of measures in Lipschitz differentability spaces, J. Amer. Math. Soc. 28 (2015), 421482.Google Scholar
Bate, D., Purely unrectifiable metric spaces and perturbations of Lipschitz functions, Acta Math. 224 (2020), 165.Google Scholar
Bate, D., Characterising rectifiable metric spaces using tangent measures, arXiv:2109.12371.Google Scholar
Bate, D., On 1-regular and 1-uniform metric measure spaces, to appear.Google Scholar
Bate, D., Csörnyei, M. and Wilson, B., The Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space, Israel J. Math. 220 (2017), 175188.Google Scholar
Bate, D. and Li, S., Characterizations of rectifiable metric measure spaces, Ann. Sci. Ec. Norm. Super. (4) 50 (2017), 137.Google Scholar
Besicovitch, A. S., On the fundamental geometrical properties of linearly measurable plane sets of points, Math. Ann. 98 (1928), 422464.Google Scholar
Besicovitch, A. S., On the fundamental geometrical properties of linearly measurable plane sets of points II, Math. Ann. 115 (1938), 296329.Google Scholar
Besicovitch, A. S., On the fundamental geometrical properties of linearly measurable plane sets of points III, Math. Ann. 116 (1939), 349357.Google Scholar
Bigolin, L. M. and Vittone, D., Some remarks about parametrizations of intrinsic regular surfaces in the Heisenberg group, Publ. Mat. 54 (2010), 159172.Google Scholar
Bishop, C. J. and Jones, P. W., Harmonic measure and arclength, Ann. of Math. (2) 132 (1990), 511547.Google Scholar
Bishop, C. J. and Peres, Y., Fractals and Probability in Analysis, Cambridge University Press, 2017.Google Scholar
Blumenthal, L. M. and Menger, K., Studies in Geometry, W. H. Freeman, 1970.Google Scholar
Bojarski, B., Hajlasz, P. and Strzelecki, P., Sard’s theorem for mappings in Hölder and Sobolev spaces, Manuscripta Math. 118 (2005), 383397.Google Scholar
Bombieri, E., De Giorgi, E. and Giusti, E., Minimal cones and the Bernstein problem, Invent. Math. 7 (1969), 243268.Google Scholar
Bonfiglioli, A., Lanconelli, E. and Uguzzoni, F., Stratified Lie Groups and Potential Theory for Their Sub-Laplacians, Springer Monographs in Mathematics, 2007.Google Scholar
Borodachov, S. V., Hardin, D. P. and Saff, E. B., Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets, Trans. Am. Math. Soc. 360 (2008), 15591580.Google Scholar
Borodachov, S. V., Hardin, D. P. and Saff, E. B., Low complexity methods for discretizing manifolds via Riesz energy minimization, Found. Comput. Math. 14 (2014), 11731208.Google Scholar
Borodachov, S. V., Hardin, D. P. and Saff, E. B., Discrete Energy on Rectifiable Sets, Springer Monographs in Mathematics. Springer, 2019.CrossRefGoogle Scholar
Bortz, S., Hoffman, J., Hofmann, S., L. Luna Garcia, J. and Nyström, K., Coronizations and big pieces in metric spaces, arXiv:2008.11544.Google Scholar
Bortz, S., Hoffman, J., Hofmann, S., L. Luna Garcia, J. and Nyström, K., The corona decomposition for parabolic uniformly rectifiable sets, arXiv:2103.12497.Google Scholar
Bortz, S., Hoffman, J., Hofmann, S., L. Luna Garcia, J. and Nyström, K., Parabolic singular integrals with nonhomogeneous kernels, arXiv:2103.12830.Google Scholar
Bortz, S. and Tapiola, O., ε-approximability of harmonic functions in Lp implies uniform rectifiability, Proc. Amer. Math. Soc. 147 (2019), 21072121.Google Scholar
Bourgain, J., On the Hausdorff dimension of harmonic measure in higher dimension, Invent. Math. 87 (1987), 477483.Google Scholar
Brakke, K. A., The motion of a surface by its mean curvature, Mathematical Notes, 20. Princeton University Press, 1978.Google Scholar
Brothers, J. E., The (ϕ, k) rectifiable subsets of a homogeneous space, Acta Math. 122 (1969), 197229.Google Scholar
Brue, E., Naber, A. and Semola, D., Boundary regularity and stability for spaces with Ricci bounded below, arXiv:2011.08383.Google Scholar
Brue, E., Pasqualetto, E. and Semola, D., Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K, N) spaces, arXiv:1909.00381, to appear in J. Eur. Math. Soc.Google Scholar
Brue, E., Pasqualetto, E. and Semola, D., Rectifiability of RCD(K,N) spaces via δ-splitting maps, Ann. Fenn. Math. 46 (2021), 465482.Google Scholar
Calderón, A., Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 13241327.Google Scholar
Cao, M., Hidalgo-Palencia, P. and Martell, J. M., Carleson measure estimates, corona decompositions, and perturbation of elliptic operators without connectivity, arXiv:2202.06363.Google Scholar
Capogna, L., Danielli, D., Pauls, S. D. and Tyson, J. T., An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, Birkhäuser, 2007.Google Scholar
Chang, A. and Tolsa, X., Analytic capacity and projections, J. Eur. Math. Soc. 22 (2020), 41214159.Google Scholar
Chang, A., Dabrowski, D., Orponen, T. and Villa, M., Structure of sets with nearly maximal Favard length, arXiv:2203.01279.Google Scholar
Cheeger, J., Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999), 428517.Google Scholar
Cheeger, J. and Colding, T., On the structure of spaces with Ricci curvature bounded below, I, J. Differential Geom. 46 (1997), 406480.Google Scholar
Cheeger, J., Colding, T. and Tian, G., On the singularities of spaces with bounded Ricci curvature, Geom. Funct. Anal. 12 (2002), 873914.Google Scholar
Cheeger, J., Jiang, W. and Naber, A., Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below, Ann. of Math. (2) 193 (2021), 407538.Google Scholar
Cheeger, J. and Naber, A., Regularity of Einstein manifolds and the codimension 4 conjecture, Ann. of Math. (2) 182 (2015), 10931165.Google Scholar
Chlebik, M., Lower s densities and rectifiability in n-space, preprint.Google Scholar
Chousionis, V., Singular integrals on Sierpinski gaskets, Publ. Mat. 53 (2009), 245256.Google Scholar
Chousionis, V., Fässler, K. and Orponen, T., Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group, Amer. J. Math. 141 (2019), 10871147.Google Scholar
Chousionis, V., Fässler, K. and Orponen, T., Boundedness of singular integrals on C1,α intrinsic graphs in the Heisenberg group, Adv. Math. 354 (2019), 106745.Google Scholar
Chousionis, V., Garnett, J., Le, T. and Tolsa, X., Square functions and uniform rectifiability, Trans. Amer. Math. Soc. 368 (2016), 60636102.Google Scholar
Chousionis, V. and Li, S., Nonnegative kernels and 1-rectifiability in the Heisenberg group, Anal. PDE 10 (2017), 14071428.Google Scholar
Chousionis, V., Li, S. and Young, R., The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups, arXiv:2004.11447.Google Scholar
Chousionis, V., Li, S. and Zimmerman, S., The traveling salesman theorem in Carnot groups, Calc. Var. Partial Differential Equations 58 (2019), Paper No. 14, 35 pp.Google Scholar
Chousionis, V., Li, S. and Zimmerman, S., Singular integrals on C1,α regular curves in Carnot groups, arXiv:1912.13279, to appear in Journal d’Analyse.Google Scholar
Chousionis, V., Magnani, V. and Tyson, J. T., On uniform measures in the Heisenberg group, Adv. Math. 363 (2020), 106980.CrossRefGoogle Scholar
Chousionis, V., Mateu, J., Prat, L. and Tolsa, X., Calderón-Zygmund kernels and rectifiability in the plane, Adv. Math. 231 (2012), 535568.Google Scholar
Chousionis, V. and Mattila, P., Singular integrals on Ahlfors-David regular subsets of the Heisenberg group, J. Geom. Anal. 21 (2011), 5677.Google Scholar
Chousionis, V. and Mattila, P., Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups, J. Reine Angew. Math. 691 (2014), 2960.Google Scholar
Chousionis, V. and Tyson, J. T., Marstrand’s density theorem in the Heisenberg group, Bull. Lond. Math. Soc. 47 (2015), 771788.Google Scholar
Chousionis, V. and Urbanski, M., Homogeneous kernerls and self-similar sets, Indiana Univ. Math. J. 64 (2015), 411431.Google Scholar
Christ, M., Lectures on singular integral operators, CBMS Regional Conference Series in Mathematics 77. Published for the Conference Board of the Mathematical Sciences, by the American Mathematical Society, 1990.Google Scholar
Christ, M., A T (b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990), 601628.Google Scholar
Christensen, J. P. R., Uniform measures and spherical harmonics, Math. Scand. 26 (1970), 293302.Google Scholar
Chunaev, P., A new family of singular integral operators whose L2-boundedness implies rectifiability, J. Geom. Anal. 27 (2017), 27252757.Google Scholar
Chunaev, P., Mateu, J. and Tolsa, X., Singular integrals unsuitable for the curvature method whose L2-boundedness still implies rectifiability, J. Anal. Math. 138 (2019), 741764.Google Scholar
Coifman, R. R., McIntosh, A. and Meyer, Y., L’intégrale de Cauchy définit un opérateur borné sur L2 pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), 361387.Google Scholar
Coifman, R. R. and Weiss, G., Analyse harmonique non-commutative sur certains espaces homogénes, Lecture Notes in Math. 242, Springer, 1971.Google Scholar
Colding, T. H. and Minicozzi II, W. P., Uniqueness of blowups and Łojasiewicz inequalities, Ann. of Math. (2) 182 (2015), 221285.Google Scholar
Colding, T. H. and Minicozzi II, W. P., The singular set of mean curvature flow with generic singularities, Invent. Math. 204 (2016), 443471.Google Scholar
Colding, T. H., Minicozzi II, W. P. and Pedersen, E. K., Mean curvature flow, Bull. Amer. Math. Soc. (N.S.) 52 (2015), 297333.Google Scholar
Colding, T. H. and Naber, A., Characterization of tangent cones of noncollapsed limits with lower Ricci bounds and applications, Geom. Funct. Anal. 23 (2013), 134148.Google Scholar
Cole, D. R. and Pauls, S., C1 hypersurfaces of the Heisenberg group are Nrectifiable, Houston J. Math. 32 (2006), 713724.Google Scholar
Csörnyei, M. and Preiss, D., Sets of finite H1 measure that intersect positively many lines in infinitely many points, Ann. Acad. Sci. Fenn. 32 (2007), 545548.Google Scholar
Csörnyei, M., Preiss, D. and Tiser, J., Lipschitz functions with unexpectedly large sets of nondifferentiability points, Abstr. Appl. Anal. (2005), 361373.Google Scholar
Dabrowski, D., Necessary condition for rectifiability involving Wasserstein distance W2, Int. Math. Res. Not. IMRN (2020), no. 22, 89368972.Google Scholar
Dabrowski, D., Cones, rectifiability, and singular integral operators, Rev. Mat. Iberoam., published online, 2021, DOI:10.4171/RMI/1301, arXiv:2006.14432.Google Scholar
Dabrowski, D., Sufficient condition for rectifiability involving Wasserstein distance W2, J. Geom. Anal. 31 (2021), 85398606.Google Scholar
Dabrowski, D., Two examples related to conical energies, Ann. Fenn. Math. 47 (2022), 261281Google Scholar
Dabrowski, D. and Tolsa, X., The measures with L2-bounded Riesz transform satisfying a subcritical Wolff-type energy condition, arXiv:2106.00303.Google Scholar
Dabrowski, D. and Villa, M., Analytic capacity and dimension of sets with plenty of big projections, arXiv:2204.05804.Google Scholar
Dahlberg, B., Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 275288.Google Scholar
Das, T., Simmons, D. and Urbanski, M., Dimension rigidity in conformal structures, Adv. Math. 308 (2017), 11271186.Google Scholar
Davey, B. and Taylor, K., A Quantification of a Besicovitch Nonlinear Projection Theorem via Multiscale Analysis, J. Geom. Anal. 32 (2022), Paper No. 138, 55 pp.Google Scholar
David, G., Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. (4) 17 (1984), 157189.Google Scholar
David, G., Morceaux de graphes lipschitziens et intégrales singuliéres sur une surface, Rev. Mat. Iberoam. 4(1) (1988), 73114.Google Scholar
David, G., Wavelets and Singular Integrals on Curves and Surfaces, Lecture Notes in Mathematics 1465. Springer-Verlag, 1991.Google Scholar
David, G., Unrectifiable 1-sets have vanishing analytic capacity, Rev. Mat. Iberoam. 14 (1998), 369479.Google Scholar
David, G., Des intégrales singuliéres bornées sur un ensemble de Cantor, C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), 391396.Google Scholar
David, G., Singular Sets of Minimizers for the Mumford-Shah Functional, Progress in Mathematics 233. Birkhäuser Verlag, 2005.Google Scholar
David, G., Local Regularity Properties of Almost- and Quasiminimal Sets with a Sliding Boundary Condition, Astérisque No. 411 (2019).Google Scholar
David, G., Engelstein, M. and Mayboroda, S., Square functions, non-tangential limits and harmonic measure in co-dimensions larger than one, Duke Math. J. 170 (2021), 455501.Google Scholar
David, G., Engelstein, M. and Toro, T., Free boundary regularity for almostminimizers, Adv. Math. 350 (2019), 11091192.Google Scholar
David, G., Feneuil, J. and Mayboroda, S., Elliptic Theory for Sets with Higher Codimensional Boundaries, Mem. Amer. Math. Soc. 274, American Mathematical Society, 2021.Google Scholar
David, G. and Mattila, P., Removable sets for Lipschitz harmonic functions in the plane, Rev. Mat. Iberoam. 10 (2000), 137215.Google Scholar
David, G. and Mayboroda, S., Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets, arXiv:2006.14661.Google Scholar
David, G. and Mayboroda, S., Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions, arXiv:2010.09793.Google Scholar
David, G. and Semmes, S., Singular integrals and rectifiable sets in Rn: Au-delàdes graphes lipschitziens, Astérisque (1991).Google Scholar
David, G. and Semmes, S., Analysis of and on Uniformly Rectifiable Sets, Mathematical Surveys and Monographs 38, American Mathematical Society, 1993.Google Scholar
David, G. and Semmes, S., Uniform rectifiability and singular sets, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 383443.Google Scholar
David, G. and Semmes, S., Quasiminimal surfaces of codimension 1 and John domains, Pacific J. Math. 183 (1998), 213277.Google Scholar
David, G. and Semmes, S., Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension, Mem. Amer. Math. Soc. 687, American Mathematical Society, 2000.Google Scholar
David, G. and Toro, T., Reifenberg Parameterizations for Sets with Holes, Mem. Amer. Math. Soc. 215, no. 1012, American Mathematical Society, 2012.Google Scholar
David, G. C., Tangents and rectifiability of Ahlfors regular Lipschitz differentiability spaces, Geom. Funct. Anal. 25 (2015), 553579.Google Scholar
David, G. C. and Kleiner, B., Rectifiability of planes and Alberti representations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), 723756.Google Scholar
David, G. C. and Le Donne, E., A note on topological dimension, Hausdorff measure, and rectifiability, Proc. Amer. Math. Soc. (2020), 42994304.Google Scholar
David, G. C. and Schul, R., A sharp necessary condition for rectifiable curves in metric spaces, Rev. Mat. Iberoam. 37 (2021), 10071044.Google Scholar
De Giorgi, E., Nuovi teoremi relativi alle misure (r − 1)-dimensionale in uno spazio ad r-dimensioni, Ricerche Mat. 4 (1955), 95113.Google Scholar
De Giorgi, E., Selected Papers, edited by Ambrosio, L., Dal Maso, G., Forti, M., Miranda, M. and Spagnolo, S., Springer-Verlag, 2005.Google Scholar
De Guzmán, M., Real Variable Methods in Harmonic Analysis, North-Holland, 1981.Google Scholar
De Lellis, C., Rectifiable Sets, Densities and Tangent Measures, Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), 2008.Google Scholar
De Lellis, C., The size of the singular set of area-minimizing currents, Surveys in differential geometry 2016. Advances in geometry and mathematical physics, 183, Surv. Differ. Geom. 21, Int. Press, 2016.Google Scholar
De Lellis, C., The regularity theory for the area functional (in geometric measure theory), arXiv:2110.11324.Google Scholar
De Lellis, C., Ghiraldin, F. and Maggi, F., A direct approach to Plateau’s problem, J. Eur. Math. Soc. 19 (2017), 22192240.Google Scholar
De Lellis, C., Hirsch, J., Marchese, A., Spolaor, L. and Stuvard, S., Fine structure of the singular set of area minimizing hypersurfaces modulo p, arXiv:2201.10204.Google Scholar
De Lellis, C., Marchese, A., Spadaro, E. and Valtorta, D., Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps, Comment. Math. Helv. 93 (2018), 737779.Google Scholar
Lellis, C. De and Otto, S., Structure of entropy solutions to the eikonal equation, J. Eur. Math. Soc. 5 (2003), 107145.Google Scholar
De Lellis, C., Otto, S. and Westdickenberg, M., Structure of entropy solutions to the eikonal equation, Arch. Ration. Mech. Anal. 170 (2003), 137184.Google Scholar
Lellis, C. De and Riviére, T., The rectifiability of entropy measures in one space dimension, J. Math. Pures Appl. 82 (2003), 13431367.Google Scholar
Delladio, S., Density rate of a set, application to rectifiability results for measurable jets, Manuscripta Math. 142 (2013), 475489.Google Scholar
Delladio, S., The set of regular values (in the sense of Clarke) of a Lipschitz map, A sufficient condition for rectifiability of class C3, Ann. Polon. Math. 117 (2016), 215230.Google Scholar
Del Nin, G. and Idu, K. O., Geometric criteria for C1,α-rectifiability, arXiv:1909.10625.Google Scholar
Del Nin, G. and Merlo, A., Endpoint Fourier restriction and unrectifiability, Proc. Amer. Math. Soc. 150 (2022), 21372144.Google Scholar
De Pauw, T., An example pertaining to the failure of the Besicovitch-Federer structure theorem in Hilbert space, Publ. Mat. 61 (2017), 153173.Google Scholar
De Philippis, G., De Rosa, A. and Ghiraldin, F., Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies, Comm. Pure Appl. Math. 71 (2018), 11231148.Google Scholar
De Philippis, G., Engelstein, M., Spolaor, L. and Velichkov, B., Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries, arXiv:2107.12485.Google Scholar
Philippis, G. De and Rindler, F., On the structure of A-free measures and applications, Ann. of Math. (2) 184 (2016), 10171039.Google Scholar
Philippis, G. De and Rindler, F., On the Structure of Measures Constrained by Linear PDEs, Proceedings of the International Congress of Mathematicians— Rio de Janeiro 2018. Vol. III. Invited lectures, 22152239, World Sci. Publ., 2018.Google Scholar
Di Donato, D., Fässler, K. and Orponen, T., Metric rectifiability of H-regular surfaces with Hölder continuous horizontal normal, to appear in IMRN, arXiv:1906.10215.Google Scholar
Dindos, M., Dyer, L. and Hwang, S., Metric rectifiability of H-regular surfaces with Hölder continuous horizontal normal, arXiv:1805.07270.Google Scholar
Don, S., Donne, Le, Moisala, T. and Vittone, D., A rectifiability result for finiteperimeter sets in Carnot groups, arXiv:1912.00493.Google Scholar
Don, S., Massacessi, A. and Vittone, D., Rank-one theorem and subgraphs of BV functions in Carnot groups, J. Funct. Anal. 276 (2019), 687715.Google Scholar
Dorronsoro, J. R., A characterization of potential spaces, Proc. Amer. Math. Soc. 95 (1985), 2131.Google Scholar
Dudziak, J., Vitushkin’s Conjecture for Removable Sets, Springer-Verlag, 2010.Google Scholar
Edelen, N. and Engelstein, M., Quantitative stratification for some free-boundary problems, Trans. Amer. Math. Soc. 371 (2019), 20432072.Google Scholar
Edelen, N., Naber, A. and Valtorta, D., Quantitative Reifenberg theorem for measures, arXiv:1612.08052.Google Scholar
Edelen, N., Naber, A. and Valtorta, D., Effective Reifenberg theorems in Hilbert and Banach spaces, Math. Ann. 374 (2019), 11391218.Google Scholar
Eiderman, V., Nazarov, F. and Volberg, A., The s-Riesz transform of an sdimensional measure in R2 is unbounded for 1 < s < 2, J. Anal. Math. 122 (2014), 123.Google Scholar
Eilenberg, S. and Harrold, O. G. Jr., Continua of finite linear measure I, Am. J. Math. 65 (1943), 137146.Google Scholar
Eriksson-Bique, S., A new Hausdorff content bound for limsup sets, arXiv:2201.13412.Google Scholar
Evans, L. C. and Gariepy, R. F., Measure Theory and Fine Properties of Functions, CRC Press, 1992.Google Scholar
Falconer, K. J., Geometry of Fractal Sets, Cambridge University Press, 1985.Google Scholar
Farag, H. M., The Riesz kernels do not give rise to higher-dimensional analogues of the Menger-Melnikov curvature, Publ. Mat. 43 (1999), 251260.Google Scholar
Farag, H. M., Unrectifiable 1-sets with moderate essential flatness satisfy Besicovitch’s 1/2-conjecture, Adv. Math. 149 (2000), 89129.Google Scholar
Farag, H. M., Curvatures of the Melnikov type, Hausdorff dimension, rectifiability, and singular integrals on Rn, Pacific J. Math. 196 (2000), 317339.Google Scholar
Farag, H. M., On the ½-problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth, Rev. Mat. Iberoam. 18 (2002), 1740.Google Scholar
Fässler, K. and Orponen, T., Riesz transform and vertical oscillation in the Heisenberg group, to appear in Anal. PDE, arXiv:1810.13122.Google Scholar
Fässler, K. and Orponen, T., Dorronsoro’s theorem in Heisenberg groups, Bull. Lond. Math. Soc. 52 (2020), 472488.Google Scholar
Fässler, K. and Orponen, T., Singular integrals on regular curves in the Heisenberg group, J. Math. Pures Appl. 153 (2021), 30113.Google Scholar
Fässler, K., Orponen, T. and Rigot, S., Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group, Trans. Amer. Math. Soc. 373 (2020), 5957– 5996.Google Scholar
Federer, H., The (φ, k) rectifiable subsets of n space, Trans. Amer. Math. Soc. 62 (1947), 114192.Google Scholar
Federer, H., Dimension and measure, Trans. Amer. Math. Soc. 62 (1947), 536– 547.Google Scholar
Federer, H., A note on the Gauss-Green theorem, Proc. Amer. Math. Soc. 9 (1958), 447451.Google Scholar
Federer, H., Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418491.Google Scholar
Federer, H., Geometric Measure Theory, Springer-Verlag, 1969.Google Scholar
Federer, H., The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc. 76 (1970), 767771.Google Scholar
Federer, H. and Fleming, W. H., Normal and integral currents, Ann. of Math. (2) 72 (1960), 458520.Google Scholar
Feneuil, J., Absolute continuity of the harmonic measure on low dimensional rectifiable sets, arXiv:2006.03118.Google Scholar
Fonseca, I. and Müller, S., A-quasiconvexity, lower semicontinuity, and Young measures, SIAM J. Math. Anal. 30 (1999), 13551390.Google Scholar
Fouladgar, K. and Simon, L., The symmetric minimal surface equation, Indiana Univ. Math. J. 69 (2020), 331366.Google Scholar
Fragala, B. and Mantegazza, R., On some notions of tangent space to a measure, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), 331342.Google Scholar
Franchi, B., Marchi, M. and Serapioni, R., Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem, Anal. Geom. Metr. Spaces 2 (2014), 258281.Google Scholar
Franchi, B. and Serapioni, R., Intrinsic Lipschitz graphs within Carnot groups, J. Geom. Anal. 26 (2016), 19441994.Google Scholar
Franchi, B., Serapioni, R. and Serra Cassano, F., Rectifiability and perimeter in the Heisenberg group, Math. Ann. 321 (2001), 479531.Google Scholar
Franchi, B., Serapioni, R. and Serra Cassano, F., On the structure of finite perimeter sets in step 2 Carnot groups, J. Geom. Anal. 13 (2003), 421466.Google Scholar
Franchi, B., Serapioni, R. and Serra Cassano, F., Intrinsic Lipschitz graphs in Heisenberg groups, J. Nonlinear Convex Anal. 7 (2006), 423441.Google Scholar
Franchi, B., Serapioni, R. and Serra Cassano, F., Regular submanifolds, graphs and area formula in Heisenberg groups, Adv. Math. 211 (2007), 152203.Google Scholar
Franchi, B., Serapioni, R. and Serra Cassano, F., Differentiability of intrinsic Lipschitz functions within Heisenberg groups, J. Geom. Anal. 21 (2011), 10441084.Google Scholar
Fuhrmann, G. and Wang, J., Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent, Discrete Contin. Dyn. Syst. 37 (2017), no. 11, 57475761.Google Scholar
Galeski, J., Besicovitch-Federer projection theorem for continuously differentiable mappings having constant rank of the Jacobian matrix, Math. Z. 289 (2018), 9951010.Google Scholar
Garnett, J., Analytic capacity and measure, Lecture Notes in Math. 297, Springer-Verlag, 1972.Google Scholar
Garnett, J., Killip, R. and Schul, R., A doubling measure on Rd can charge a rectifiable curve, Proc. Amer. Math. Soc. 138 (2010), 16731679.Google Scholar
Garnett, J. B. and Marshall, D. E., Harmonic Measure, Cambridge University Press, 2005.Google Scholar
Garnett, J., Mourgoglou, M. and Tolsa, X., Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions, Duke Math. J. 167 (2018), 14731524.Google Scholar
Ghinassi, S., Sufficient conditions for C1,α parametrization and rectifiability, Ann. Acad. Sci. Fenn. Math. 45 (2020), 10651094.Google Scholar
Ghinassi, S. and Goering, M., Menger curvatures and C1,α rectifiability of measures, Arch. Math. (Basel) 114 (2020), 419429.Google Scholar
Girela-Sarrión, D., Geometric conditions for the L2-boundedness of singular integral operators with odd kernels with respect to measures with polynomial growth in Rd, J. Anal. Math. 137 (2019), 339372.Google Scholar
Girela-Sarrión, D. and Tolsa, X., The Riesz transform and quantitative rectifiability for general Radon measures, Calc. Var. Partial Differential Equations 57 (2018), Paper No. 16, 63 pp.Google Scholar
Giusti, E., Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1984.Google Scholar
Gromov, M., Structures métriques pour les variétés riemanniennes, Edited by Lafontaine, J. and Pansu, P.. Textes Mathématiques 1. CEDIC, Paris, 1981.Google Scholar
Hahlomaa, I., Menger curvature and Lipschitz parametrizations in metric spaces, Fund. Math. 185 (2005), 143169.Google Scholar
Hahlomaa, I., Menger curvature and rectifiability in metric spaces, Adv. Math. 219 (2008), 18941915.Google Scholar
Hajlasz, P., On an old theorem of Erdös about ambiguous locus, arXiv:2011.14508.Google Scholar
Hardin, D. P., B. Saff and O. V. Vlasiuk, E., Asymptotics of k-nearest neighbor Riesz energies, arXiv:2201.00474.Google Scholar
Hensel, S. and Laux, T., A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness, arXiv:2109.04233.Google Scholar
Hirsch, J., Stuvard, S. and Valtorta, D., Rectifiability of the singular set of multiple valued energy minimizing harmonic maps, Trans. Amer. Math. Soc. 371 (2019), 43034352.Google Scholar
Hofmann, S., Le, P., M. Martell, J. and Nyström, K., The weak-A property of harmonic and p-harmonic measures implies uniform rectifiability, Anal. PDE 10 (2017), 513558.Google Scholar
Hofmann, S., Lewis, J. and Nyström, K., Existence of big pieces of graphs for parabolic problems, Ann. Acad. Sci. Fenn. Math. 28 (2003), 355384.Google Scholar
Hofmann, S., Lewis, J. and Nyström, K., Caloric measure in parabolic flat domains, Duke Math. J. 122 (2004), 281345.Google Scholar
Hofmann, S., M. Martell, J. and Mayboroda, S., Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions, Duke Math. J. 165 (2016), 23312389.Google Scholar
Hofmann, S., Martell, J. M., Mayboroda, S., Toro, T. and Zhao, Z., Uniform rectifiability and elliptic operators satisfying a Carleson measure condition, Geom. Funct. Anal. 31 (2021), 325401.Google Scholar
Hofmann, S. and Tapiola, O., Uniform rectifability and ε-approximability of harmonic functions in Lp, Ann. Inst. Fourier (Grenoble) 70 (2020), 15951638.Google Scholar
Hovila, R., Transversality of isotropic projections, unrectifiability, and Heisenberg groups, Rev. Mat. Iberoam. 102 (2014), 463476.Google Scholar
Hovila, R., Järvenpää, E., Järvenpää and F. Ledrappier, M., Transversality of isotropic projections, unrectifiability, and Heisenberg groups, Rev. Mat. Iberoam. 102 (2014), 436476.Google Scholar
Huisken, G., Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990), 285299.Google Scholar
Huovinen, P., Singular integrals and rectifiability of measures in the plane, Ann. Acad. Sci. Fenn. Math. Diss. No. 109 (1997), 63 pp.Google Scholar
Huovinen, P., A nicely behaved singular integral on a purely unrectifiable set, Proc. Amer. Math. Soc. 129 (2001), 33453351.Google Scholar
Hyde, M., A d-dimensional Analyst’s Travelling Salesman Theorem for subsets of Hilbert space, arXiv:2106.12661.Google Scholar
Hyde, M., The restricted content and the d-dimensional Analyst’s Travelling Salesman Theorem for general sets, Adv. Math. 397 (2022), Paper No. 108189.Google Scholar
Idu, K. O., Magnani, V. and Maiale, F. P., Characterizations of k-rectifiability in homogenous groups, J. Math. Anal. Appl. 500 (2021), Paper No. 125120.Google Scholar
Idu, K. O. and Maiale, F. P., C1,α-rectifiability in low codimension in Heisenberg groups, arXiv:2102.05165.Google Scholar
Ilmanen, T., Convergence of the Allen-Cahn equation to Brakke’s motion by mean curvature, J. Differential Geom. 38 (1993), 417461.Google Scholar
Ilmanen, T., Elliptic Regularization and Partial Regularity for Motion by Mean Curvature, Mem. Amer. Math. Soc. 108, American Mathematical Society, 1994.Google Scholar
Isakov, N. M., On a global property of approximately differentiable functions, Mat. Zametki 41 (1987), 500508, 620.Google Scholar
Jaye, B. and Merchán, T., On the problem of existence in principal value of a Calderón-Zygmund operator on a space of non-homogeneous type, Proc. Lond. Math. Soc. (3) 121 (2020), 152176.Google Scholar
Jaye, B. and Merchán, T., Small local action of singular integrals on spaces of non-homogeneous type, Rev. Mat. Iberoam. 36 (2020), 21832207.Google Scholar
Jaye, B. and Merchán, T., The Huovinen transform and rectifiability of measures, Adv. Math. 400 (2022), Paper No. 108297.Google Scholar
Jaye, B. and Nazarov, F., Reflectionless measures and the Mattila-Melnikov-Verdera uniform rectifiability theorem, In Geometric Aspects of Functional Analysis, 199229, Lecture Notes in Math. 2116, Springer, 2014.Google Scholar
Jaye, B. and Nazarov, F., Three revolutions in the kernel are worse than one, Int. Math. Res. Not. IMRN 2018, 73057317.Google Scholar
Jaye, B. and Nazarov, F., Reflectionless measures for Calderón-Zygmund operators II: Wolff potentials and rectifiability, J. Eur. Math. Soc. 21 (2019), 549583.Google Scholar
Jaye, B., Nazarov, F. and Tolsa, X., The measures with an associated square function operator bounded in L2, Adv. Math. 339 (2018), 60112.Google Scholar
Jaye, B., Tolsa, X. and Villa, M., A proof of Carleson’s ε2-conjecture, Ann. of Math. (2) 194 (2021), 97161.Google Scholar
Jerrard, R. L., A new proof of the rectifiable slices theorem, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002), 905924.Google Scholar
Jiang, W. and Naber, A., L2 curvature bounds on manifolds with bounded Ricci curvature, Ann. of Math. (2) 193 (2021), 107222.Google Scholar
Jones, P. W., Rectifiable sets and traveling salesman problem, Invent. Math. 102 (1990), 115.Google Scholar
Jones, P. W., H. Katz, N. and Vargas, A., Checkerboards, Lipschitz functions and uniform rectifiability, Rev. Mat. Iberoam. 13 (1997), 189210.Google Scholar
Jones, P. W. and Murai, T., Positive analytic capacity but zero Buffon needle probability, Pacific J. Math. 133 (1988), 99114.Google Scholar
Joyce, H. and Mörters, P., A set with finite curvature and projections of zero length, J. Math. Anal. Appl. 247 (2000), 126135.Google Scholar
Julia, A. and Merlo, A., On sets with unit Hausdorff density in homogeneous groups, arXiv:2203.16471.Google Scholar
Julia, A., Nicolussi Golo, S. and Vittone, D., Area of intrinsic graphs and coarea formula in Carnot groups, arXiv:2004.02520.Google Scholar
Julia, A., Nicolussi Golo, S. and Vittone, D., Nowhere differentiable intrinsic Lipschitz graphs, Bull. Lond. Math. Soc. 53 (2021), 17661775.Google Scholar
Julia, A., Nicolussi Golo, S. and Vittone, D., Lipschitz functions on submanifolds in Heisenberg groups, arXiv:2107.00515.Google Scholar
Käenmäki, A., Dynamics of the scenery flow and conical density theorems, In Dynamical Systems, 99143, Banach Center Publ. 115, Polish Acad. Sci. Inst. Math., 2018.Google Scholar
Käenmäki, A., Sahlsten, T. and Shmerkin, P., Dynamics of the scenery flow and geometry of measures, Proc. Lond. Math. Soc. (3) 110 (2015), 12481280.Google Scholar
Keith, S., A differentiable structure for metric measure spaces, Adv. Math. 183 (2004), 271315.Google Scholar
Keleti, T., A peculiar set in the plane constructed by Vitushkin, Ivanov and Melnikov, Real. Anal. Exch. 20 (1995), 291312.Google Scholar
Kenig, C., Preiss, D. and Toro, T., Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions, J. Amer. Math. Soc. 22 (2009), 771796.Google Scholar
Kirchheim, B., Rectifiable metric spaces: Local structure and regularity of Hausdorff measure, Proc. Amer. Math. Soc. 121 (1994), 113123.Google Scholar
Kirchheim, B. and Preiss, D., Uniformly distributed measures in Euclidean spaces, Math. Scand. 90 (2002), 152160.Google Scholar
Kirchheim, B. and Serra Cassano, F., Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group, Ann. Sc. Norm. Super. Pisa Cl. Sci. 3 (2004), 871896.Google Scholar
Kohn, R. V., An example concerning approximate differentiation, Indiana Univ. Math. J. 26 (1977), 393397.Google Scholar
Kolasinski, O., Higher order rectifiability of measures via averaged discrete curvatures, Rev. Mat. Iberoam. 33 (2017), 861884.Google Scholar
Kowalski, O. and Preiss, D., Besicovitch type properties of measures and submanifolds, J. Reine Angew. Math. 379 (1987), 115151.Google Scholar
Krantz, S. G. and Parks, H. R., Geometric Integration Theory, Birkhäuser, 2008.Google Scholar
Kun, G., Maleva, O. and Máthé, A., Metric characterization of pure unrectifiability, Real Anal. Exchange 31 (2005/2006), 195213.Google Scholar
Lahti, P., Federer’s characterization of sets of finite perimeter in metric spaces, Anal. PDE 13, (2020), 15011519.Google Scholar
Lang, U., Local currents in metric spaces, J. Geom. Anal. 21 (2011), 683742.Google Scholar
Donne, E. Le and Young, R., Carnot rectifiability of sub-Riemannian manifolds with constant tangent, arXiv:1901.1122.Google Scholar
Lee, M.-C., Naber, A. and Neumayer, R., dp convergence and ε-regularity theorems for entropy and scalar curvature lower bounds, arXiv:2010.15663.Google Scholar
Léger, J. C., Rectifiability and Menger curvature, Ann. of Math. 149 (1999), 831– 869.Google Scholar
Lerman, G., Quantifying curvelike structures of measures by using L2 Jones quantities, Comm. Pure Appl. Math. 56 (2003), 12941365.Google Scholar
Lerman, G. and Whitehouse, J. T., High-dimensional Menger-type curvatures. Part I: Geometric multipoles and multiscale inequalities, Rev. Mat. Iberoam. 27 (2011), 493555.Google Scholar
Li, S., Stratified β-numbers and traveling salesman in Carnot groups, arXiv:1902.03268.Google Scholar
Li, S. and Naber, A., Quantitative estimates on the singular sets of Alexandrov spaces, Peking Math. J. 3 (2020), 203234.Google Scholar
Li, S. and Schul, R., The traveling salesman problem in the Heisenberg group: upper bounding curvature, Trans. Amer. Math. Soc. 368 (2016), 45854620.Google Scholar
Li, S. and Schul, R., An upper bound for the length of a traveling salesman path in the Heisenberg group, Rev. Mat. Iberoam. 32 (2016), 391417.Google Scholar
Lin, F., Mapping problems, fundamental groups and defect measures, Acta Math. Sin. (Engl. Ser.) 15 (1999), 2552.Google Scholar
Lin, F., Gradient estimates and blow-up analysis for stationary harmonic maps, Ann. of Math. (2) 149 (1999), 785829.Google Scholar
Lin, F. and Yang, X., Geometric Measure Theory; an Introduction, International Press, 2002.Google Scholar
Lorent, A., Rectifiability of measures with locally uniform cube density, Proc. London. Math. Soc. (3) 86 (2003), 153249.Google Scholar
Maggi, F., Sets of Finite Perimeter and Variational Problems, Cambridge University Press, 2012.Google Scholar
Magnani, V., Unrectifiability and rigidity in stratified groups, Arch. Math. (Basel) 83 (2004), 568576.Google Scholar
Magnani, V., Characteristic points, rectifiability and perimeter measure on stratified groups, J. Eur. Math. Soc. 8 (2006), 585609.Google Scholar
Magnani, V., Some remarks on densities in the Heisenberg group, Ann. Acad. Sci. Fenn. Math. 42 (2017), 357365.Google Scholar
Maleva, O. and Preiss, D., Cone unrectifiable sets and non-differentiability of Lipschitz functions, Israel J. Math. 232 (2019), 75108.Google Scholar
Mantegazza, V., Lecture Notes on Mean Curvature Flow, Progress in Mathematics 290. Birkhäuser/Springer Basel AG, 2011.Google Scholar
Marchese, A. and Merlo, A., Characterization of rectifiability via Lusin type approximation, arXiv:2112.15376.Google Scholar
Marconi, E., The rectifiability of the entropy defect measure for Burgers equation, arXiv:2004.09932.Google Scholar
Marconi, E., Rectifiability of entropy defect measures in a micromagnetics model, arXiv:2011.13065.Google Scholar
Marstrand, J. M., Hausdorff two-dimensional measure in 3 space, Proc. London. Math. Soc. (3) 11 (1961), 91108.Google Scholar
Marstrand, J. M., The (φ, s) regular sets in n space, Trans. Amer. Math. Soc. 113 (1964), 369392.Google Scholar
Martikainen, H. and Orponen, T., Boundedness of the density normalised Jones’ square function does not imply 1-rectifiability, J. Math. Pures Appl. 110 (2018), 7192.Google Scholar
Martikainen, H. and Orponen, T., Characterising the big pieces of Lipschitz graphs property using projections, J. Eur. Math. Soc. 20 (2018), 10551073.Google Scholar
Martin, M. A. and Mattila, P., k-dimensional regularity classifications for sfractals, Trans. Amer. Math. Soc. 305 (1988), 26412648.Google Scholar
Martin, M. A. and Mattila, P., On the parametrization of self-similar and other fractal sets, Proc. Amer. Math. Soc. 128 (2000), 293315.Google Scholar
Mas, A. and Tolsa, X., Variation for the Riesz transform and uniform rectifiability, J. Eur. Math. Soc. 16 (2014), 22672321.Google Scholar
Massaccesi, H. and Vittone, D., An elementary proof of the rank-one theorem for BV functions, J. Eur. Math. Soc. 21 (2019), 32553258.Google Scholar
Mateu, J. and Prat, L., L2-bounded singular integrals on a purely unrectifiable set in Rd, Ann. Fenn. Math 46 (2021), 187200.Google Scholar
Mateu, J., Prat, L. and Tolsa, X., Removable singularities for Lipschitz caloric functions in time varying domains, arXiv:2005.03397.Google Scholar
Mattila, P., Hausdorff m regular and rectifiable sets in n-space, Trans. Amer. Math. Soc. 205 (1975), 263274.Google Scholar
Mattila, P., An example illustrating integralgeometric measures, Amer. J. Math. 108 (1986), 693702.Google Scholar
Mattila, P., Smooth maps, null-sets for integralgeometric measure and analytic capacity, Ann. of Math. (2) 123 (1986), 303309.Google Scholar
Mattila, P., Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995.Google Scholar
Mattila, P., Cauchy singular integrals and rectifiability of measures in the plane, Adv. Math. 115 (1995), 134.Google Scholar
Mattila, P., Singular integrals and rectifiability, In Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000). Publ. Mat. 2002, Vol. Extra, 199208.Google Scholar
Mattila, P., Measures with unique tangent measures in metric groups, Math. Scand. 97 (2005), 298398.Google Scholar
Mattila, P., Parabolic rectifiability, tangent planes and tangent measures, to appear Ann. Fenn. Math. 47 (2022), 855884.Google Scholar
Mattila, P. and Melnikov, M. S., Existence and weak-type inequalities for Cauchy integrals of general measures on rectifiable curves and sets, Proc. Amer. Math. Soc. 120 (1994), 143149.Google Scholar
Mattila, P., S. Melnikov, M. and Verdera, V., The Cauchy integral, analytic capacity, and uniform rectifiability, Ann. of Math. (2) 144 (1996), 127136.Google Scholar
Mattila, P. and Paramonov, P. V., On geometric properties of harmonic Lip1capacity, Pacific J. Math. 171 (1995), 469490.Google Scholar
Mattila, P. and Preiss, D., Rectifiable measures in Rn and existence of principal values for singular integrals, J. London Math. Soc. 52 (1995), 482496.Google Scholar
Mattila, P., Serapioni, R. and Serra Cassano, F., Characterization of intrinsic rectifiability in Heisenberg groups, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010), 687723.Google Scholar
Mattila, P. and Verdera, J., Convergence of singular integrals with general measures, J. Eur. Math. Soc. 11 (2009), 257271.Google Scholar
Mayboroda, S. and Volberg, A., Boundedness of the square function and rectifiability, C. R. Math. Acad. Sci. Paris 347 (2009), 10511056.Google Scholar
Mayer, S. and Urbanski, M., Finer geometric rigidity of limit sets of conformal IFS, Proc. Amer. Math. Soc. 131 (2003), 36953702.Google Scholar
Melnikov, M. S., Analytic capacity: a discrete approach and the curvature of measure, (Russian) Mat. Sb. 186 (1995), 5776; translation in Sb. Math. 186 (1995), no. 6, 827846.Google Scholar
Melnikov, M. S. and Verdera, V., A geometric proof of the L2 boundedness of the Cauchy integral on Lipschitz graphs, Internat. Math. Res. Notices 1996, 325–331.Google Scholar
Menger, K., Untersuchugen über allgemaine Metrik. Vierte Untersuchung. Zur Metrik der Kurven, Math. Ann. 103 (1930), 466501.Google Scholar
Menne, U., Second order rectifiability of integral varifolds of locally bounded first variation, J. Geom. Anal. 23 (2013), 709763.Google Scholar
Menne, U., Pointwise differentiability of higher order for sets, Ann. Global Anal. Geom. 55 (2019), 591621.Google Scholar
Menne, U., Pointwise differentiability of higher order for distributions, Anal. PDE 14 (2021), 323354.Google Scholar
Menne, U. and Santilli, M., A geometric second-order-rectifiable stratification for closed subsets of Euclidean space, Ann. Sc. Norm. Super. Pisa Cl. Sci. 19 (2019), 11851198.Google Scholar
Merhej, J., On the geometry of rectifiable sets with Carleson and Poincaré-type conditions, Indiana Univ. Math. J. 66 (2017), 16591706.Google Scholar
Merlo, A., Marstrand-Mattila rectifiability criterion for 1-codimensional measures in Carnot Groups, arXiv:2007.03236.Google Scholar
Merlo, A., Geometry of 1-codimensional measures in Heisenberg groups, Invent. Math. 227 (2022), 27148.Google Scholar
Meurer, M., Integral Menger curvature and rectifiability of n-dimensional Borel sets in Euclidean N-space, Trans. Amer. Math. Soc. 370 (2018), 11851250.Google Scholar
Mickle and Radó, E. J., Density theorems for outer measures in n-space, Proc. Amer. Math. Soc. 9 (1958), 433439.Google Scholar
Minicozzi, W. P., Commentary on ‘Nonunique tangent maps at isolated singularities of harmonic maps’ by Brian White, Bull. Amer. Math. Soc. (N.S.) 55 (2018), 359362.Google Scholar
Mitrea, D., Mitrea, M. and Verdera, J., Characterizing regularity of domains via the Riesz transforms on their boundaries, Anal. PDE 9 (2016), 9551018.Google Scholar
Molero, A., Mourgoglou, M., Puliatti, C. and Tolsa, X., L2-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type, arXiv:2112.07332.Google Scholar
Mondino, A. and Naber, A., Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds, J. Eur. Math. Soc. 21 (2019), 18091854.Google Scholar
Moore, E. F., Density ratios and (φ, 1) rectifiability in n-space, Trans. Amer. Math. Soc. 69 (1950), 324334.Google Scholar
Morgan, F., Geometric Measure Theory; a Beginner’s Guide, Academic Press, 1988.Google Scholar
Morse, A. P. and Randolph, J. F., The (Φ, 1) rectifiable subsets of the plane, Trans. Amer. Math. Soc. 55 (1944), 236305.Google Scholar
Moser, R., Stationary measures and rectifiability, Calc. Var. Partial Differential Equations 17 (2003), 357368.Google Scholar
Naber, A., Lecture notes on rectifiable Reifenberg for measures, In Harmonic Analysis and Applications, 289346, IAS/Park City Math. Ser. 27, American Mathematical Society, 2020.Google Scholar
Naber, A., Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds, SIGMA Symmetry Integrability Geom. Methods Appl. 16 (2020), Paper No. 104.Google Scholar
Naber, A. and Valtorta, R., Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps, Ann. of Math. 185 (2017), 131227.Google Scholar
Naber, A. and Valtorta, R., Stratification for the singular set of approximate harmonic maps, Math. Z. 290 (2018), 14151455.Google Scholar
Naber, A. and Valtorta, R., Energy identity for stationary Yang Mills, Invent. Math. 216 (2019), 847925.Google Scholar
Naber, A. and Valtorta, R., The singular structure and regularity of stationary varifolds, J. Eur. Math. Soc. 22 (2020), 33053382.Google Scholar
Naor, A. and Young, R., Vertical perimeter versus horizontal perimeter, Ann. of Math. 188 (2018), 171279.Google Scholar
Naor, A. and Young, R., Foliated corona decompositions, arXiv:2004.12522.Google Scholar
Naples, L., Rectifiability of pointwise doubling measures in Hilbert space, arXiv:2002.07570.Google Scholar
Nazarov, F., Tolsa, X. and Volberg, A., On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1, Acta Math. 213 (2014), 237321.Google Scholar
Nazarov, F., Tolsa, X. and Volberg, A., The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions, Publ. Mat. 58 (2014), 517532.Google Scholar
Nazarov, F., Treil, S. and Volberg, A., Accretive system T b-theorems on nonhomogeneous spaces, Duke Math. J. 113 (2002), 259312.Google Scholar
Nazarov, F. and Volberg, A., On analytic capacity of portions of continuum and a theorem of Guy David, preprint, 1999, Erwin Schrodinger International Institute for Mathematical Physics, ESI 71, http://esi.ac.at/preprints/ESI-Preprints.html.Google Scholar
Nimer, A. D., A sharp bound on the Hausdorff dimension of the singular set of a uniform measure, Calc. Var. Partial Differential Equations 56 (2017), no. 4, Paper No. 111, 31 pp.Google Scholar
Nimer, A. D., Conical 3-uniform measure: a family of new examples and characterizations, to appear in J. Differential Geom., arXiv:1809.08941.Google Scholar
Nimer, A. D., Uniformly distributed measures have big pieces of Lipschitz graphs locally, Ann. Acad. Sci. Fenn. Math. 44 (2019), 389405.Google Scholar
Okikiolu, K., Characterization of subsets of rectifiable curves in Rn, J. London Math. Soc. (2) 46 (1992), 336348.Google Scholar
O’Neil, T. C., A local version of the projection theorem, Proc. London Math. Soc. (3) 73 (1996), 68104.Google Scholar
Orponen, T., The local symmetry condition in the Heisenberg group, arXiv:1807.05010.Google Scholar
Orponen, T., Rickman rugs and intrinsic bilipschitz graphs, arXiv:2011.08168.Google Scholar
Orponen, T., Plenty of big projections imply big pieces of Lipschitz graphs, Invent. Math. (2021), 157.Google Scholar
Painlevé, P., Sur les lignes singuliéres des fonctions analytiques, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 2 (1888).Google Scholar
Pajot, H., Théoréme de recouvrement par des ensembles Ahlfors-réguliers et capacité analytique, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 133135.Google Scholar
Pajot, H., Conditions quantitatives de rectifiabilité, Bull. Soc. Math. France 125 (1997), 1553.Google Scholar
Pajot, H., Analytic capacity, rectifiability, Menger curvature and the Cauchy integral, Lecture Notes in Mathematics 1799. Springer-Verlag, 2002.Google Scholar
Pansu, P., Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2) 129 (1989), 160.Google Scholar
Pauls, S., A notion of rectifiability modeled on Carnot groups, Indiana Univ. Math. J. 53 (2004), 4981.Google Scholar
Prat, L., Puliatti, C. and Tolsa, X., L2-boundedness of gradients of single layer potentials and uniform rectifiability, Anal. PDE 14 (2021), 717791.Google Scholar
Preiss, D., Geometry of Measures in Rn: distribution, rectifiability and densities, Ann. of Math. 125 (1987), 537643.Google Scholar
Preiss, D., Differentiability of Lipschitz functions on Banach spaces, J. Funct. Anal. 91 (1990), 312345.Google Scholar
Preiss, D. and Tiser, J., On Besicovitch’s 1/2-problem, J. London Math. Soc. (2) 25 (1992), 194207.Google Scholar
Pugh, H., A localized Besicovitch-Federer projection theorem, arXiv:1607.01758.Google Scholar
Qi, Y. and Zheng, G.-F., Convergence of solutions of the weighted Allen-Cahn equations to Brakke type flow, Calc. Var. Partial Differential Equations 57 (2018), Paper No. 133, 41 pp.Google Scholar
Rataj, J. and Zähle, M., General normal cycles and Lipschitz manifolds of bounded curvature, Ann. Global Anal. Geom. 27 (2005), 135156.Google Scholar
Rataj, J. and Zähle, M., Curvature Measures of Singular Sets, Springer Monographs in Mathematics, Springer, 2019.Google Scholar
Reifenberg, E. R., Solution of the Plateau Problem for m-dimensional surfaces of varying topological type, Acta Math. 104 (1960), 192.Google Scholar
Rigot, S., Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme, Mem. Soc. Math. Fr. (N.S.) No. 82 (2000).Google Scholar
Santilli, M., Rectifiability and approximate differentiability of higher order for sets, Indiana Univ. Math. J. 68 (2019), 10131046.Google Scholar
Santilli, M., Second order rectifiability of varifolds of bounded mean curvature, Calc. Var. Partial Differential Equations 60 (2021), no. 2, Paper No. 81, 17 pp.Google Scholar
Schoen, R. and Uhlenbeck, K., A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307335.Google Scholar
Schul, R., Subsets of rectifiable curves in Hilbert space – the analyst’s TSP, J. Anal. Math. 103 (2007), 331375.Google Scholar
Serapioni, R., Rectifiable sets in Carnot groups, In Geometric Methods in PDE’s, 249267, Lect. Notes Semin. Interdiscip. Mat. 7, Semin. Interdiscip. Mat. (S.I.M.), Potenza, 2008.Google Scholar
Serra Cassano, F., Some topics of geometric measure theory in Carnot groups, In Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds. Vol. 1, 1121, EMS Ser. Lect. Math., Eur. Math. Soc., 2016.Google Scholar
Simon, L., Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Volume 3, 1983.Google Scholar
Simon, L., Rectifiability of the singular set of energy minimizing maps, Calc. Var. Partial Differential Equations 3 (1995), 165.Google Scholar
Simon, L., Rectifiability of the singular sets of multiplicity 1 minimal surfaces and energy minimizing maps, Surveys in Differential Geometry 2 (Cambridge, MA, 1993), 246305, Int. Press, 1995.Google Scholar
Simon, L., Theorems on Regularity and Singularity of Energy Minimizing Maps. Based on lecture notes by Norbert Hungerbühler, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, 1996.Google Scholar
Simon, L., Stable minimal hypersurfaces in RN+1+l with singular set an arbitrary closed K in {0}× Rl, arXiv:2101.06401.Google Scholar
Simon, L., A Liouville-type theorem for stable minimal hypersurfaces, arXiv:2101.06404.Google Scholar
Simons, J., Minimal varieties in Riemannian manifolds, Ann. of Math. (2) 68 (1968), 62105.Google Scholar
Solomon, B., A new proof of the closure theorem for integral currents, Indiana Univ. Math. J. 33 (1984), 393418.Google Scholar
Stuvard, B. and Tonegawa, Y., An existence theorem for Brakke flow with fixed boundary conditions, Calc. Var. 60 (2021), paper no. 43.Google Scholar
Tao, T., A quantitative version of the Besicovitch projection theorem via multiscale analysis, Proc. London Math. Soc. (3) 98 (2009), 559584.Google Scholar
Tian, G., Gauge theory and calibrated geometry I, Ann. Math. 151 (2000), 193– 268.Google Scholar
Tolsa, X., Principal values for the Cauchy integral and rectifiability, Proc. London Math. Soc. (3) 82 (2001), 195228.Google Scholar
Tolsa, X., Painlevé’s problem and the semiadditivity of analytic capacity, Acta. Math. 90 (2003), 105149.Google Scholar
Tolsa, X., Finite curvature of arc length measure implies rectifiability: a new proof, Indiana Univ. Math. J. 54 (2005), 10751105.Google Scholar
Tolsa, X., Growth estimates for Cauchy integrals of measures and rectifiability, Geom. Funct. Anal. 17 (2007), 605643.Google Scholar
Tolsa, X., Principal values for Riesz transforms and rectifiability, J. Funct. Anal. 254 (2008), 18111863.Google Scholar
Tolsa, X., Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality, Proc. London Math. Soc. (3) 98 (2009), 393426.Google Scholar
Tolsa, X., Mass transport and uniform rectifiability, Geom. Funct. Anal. 22 (2012), 478527.Google Scholar
Tolsa, X., Analytic Capacity, the Cauchy Transform, and Non-homogeneous Caldéron-Zygmund Theory, Birkhäuser, 2014.Google Scholar
Tolsa, X., Uniform Measures and Uniform Rectifiability, J. London Math. Soc. (2) 92 (2015), 118.Google Scholar
Tolsa, X., Characterization of n-rectifiability in terms of Jones’ square function: part I, Calc. Var. Partial Differential Equations 54 (2015), no. 4, 36433665. Correction in Calc. Var. Partial Differential Equations 58 (2019), Paper No. 35.Google Scholar
Tolsa, X., Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform, Mem. Amer. Math. Soc. 245, American Mathematical Society, 2017.Google Scholar
Tolsa, X., Rectifiability of measures and the βp coeflcients, Publ. Mat. 63 (2019), 491519.Google Scholar
Tolsa, X., The measures with L2–bounded Riesz transform and the Painlevé problem for Lipschitz harmonic functions, arXiv:2106.00680.Google Scholar
Tolsa, X. and Toro, T., Rectifiability via a square function and Preiss’ theorem, Int. Math. Res. Not. IMRN 2015, 46384662.Google Scholar
Tonegawa, Y., Brakke’s Mean Curvature Flow: An Introduction, Springer-Briefs in Mathematics, Springer, 2019.Google Scholar
Toro, T., Geometric conditions and existence of bi-Lipschitz parameterizations, Duke Math. J. 77 (1995), 193227.Google Scholar
Toro, T., Geometric measure theory – recent applications, Notices Amer. Math. Soc. 66 (2019), 474481.Google Scholar
Verdera, J., A weak type inequality for Cauchy transforms of measures, Publ. Mat. 36 (1992), 10291034.Google Scholar
Verdera, J., Birth and life of the L2 boundedness of the Cauchy Integral on Lipschitz graphs, arXiv:2109.06690.Google Scholar
Villa, M., Higher dimensional Jordan curves, arXiv:1908.10289.Google Scholar
Villa, M., A square function involving the center of mass and rectifiability, arXiv:1910.13747.Google Scholar
Villa, M., Ω-symmetric measures and related singular integrals, Rev. Mat. Iberoam. 37 (2021), 16691715.Google Scholar
Vittone, D., Lipschitz graphs and currents in Heisenberg groups, Forum Math. Sigma 10 (2022), Paper No. e6.Google Scholar
Vitushkin, A. G., Analytic capacity of sets in problems of approximation theory, Uspehi Mat. Nauk. 22 (1967), 141199.Google Scholar
Vitushkin, A. G., Ivanov, L. D. and Melnikov, M. S., Incommeasurability with the minimal linear measure on the length of a set, Sov. Mat. Dokl. 4 (1963), 1160– 1164.Google Scholar
Volberg, A., Calderón-Zygmund capacities and operators on non-homogeneous spaces, Regional Conference Series in Mathematics 100, American Mathematical Society, 2003.Google Scholar
Volpert, A. I., The spaces BV and quasi-linear equations, Math. USSR Sb. 2 (1967), 225267.Google Scholar
White, B., Tangent cones to two-dimensional area-minimizing integral currents are unique, Duke Math. J. 50 (1983), 143160.Google Scholar
White, B., A new proof of the compactness theorem for integral currents, Comment. Math. Helv. 64 (1989), 207220.Google Scholar
White, B., Nonunique tangent maps at isolated singularities of harmonic maps, Bull. Amer. Math. Soc. (N.S.) 26 (1992), 125129.Google Scholar
White, B., A new proof of Federer’s structure theorem for k-dimensional subsets of RN, J. Amer. Math. Soc. 11 (1998), 693701.Google Scholar
White, B., Rectifiability of flat chains, Ann. of Math. (2) 150 (1999), 165184.Google Scholar
White, B., The size of the singular set in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 13 (2000), 665695.Google Scholar
White, B., Mean curvature flow with boundary, arXiv:1901.03008.Google Scholar
Wolff, T., Plane harmonic measures live on sets of σ-finite length, Ark. Mat. 31 (1993), 137172.Google Scholar
Wolff, T., Counterexamples with harmonic gradients, In Essays on Fourier Analysis in Honor of Elias M. Stein (Princeton, NJ, 1991), 321384, Princeton Math. Ser. 42, Princeton University Press, 1995.Google Scholar
Wu, J.-M., On singularity of harmonic measure in space, Pacific J. Math. 121 (1986), 485496.Google Scholar
Zähle, M., Integral and current representation of Federer’s curvature measures, Arch. Math. (Basel) 46 (1986), 557567.Google Scholar
Zajicek, L., On the differentiation of convex functions in finite and infinite dimensional spaces, Czechoslovak Math. J. 29 (1979), 340348.Google Scholar
Ziemer, W. P., Some remarks on harmonic measure in space, Pacific J. Math. 55 (1974), 629637.Google Scholar
Ziemer, W. P., Weakly Differentiable Functions, Springer-Verlag, 1989.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×