Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-29T06:42:16.856Z Has data issue: false hasContentIssue false

8 - Absence of singular continuous spectrum for some geometric Laplacians

Published online by Cambridge University Press:  05 May 2013

Leonardo A. Cano García
Affiliation:
Universidad de los Andes
Alexander Cardona
Affiliation:
Universidad de los Andes, Colombia
Iván Contreras
Affiliation:
Universität Zürich
Andrés F. Reyes-Lega
Affiliation:
Universidad de los Andes, Colombia
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
Geometric and Topological Methods for Quantum Field Theory
Proceedings of the 2009 Villa de Leyva Summer School
, pp. 307 - 321
Publisher: Cambridge University Press
Print publication year: 2013

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

[Bal97] E., Balslev. Spectral deformation of Laplacians on hyperbolic manifolds. Comm. Anal. Geom., 5 (2): 213–247, 1997.Google Scholar
[Can11] L., Cano. Analytic dilation on complete manifolds with corners of codimension 2. PhD thesis, University of Bonn, 2011.
[Can12] L., Cano. Mourre estimates for compatible laplacians on complete manifolds with corners of codimension 2. Ann. Global Anal. Geom., 2012.
[Cha84] I., Chavel. Eigenvalues in Riemannian geometry, Pure and Applied Mathematics 115. Orlando, FL: Academic Press, 1984. Including a chapter by Burton, Randol, with an appendix by Jozef, Dodziuk.
[DEM98] P., Duclos, P., Exner and B., Meller. Exponential bounds on curvature-induced resonances in a two-dimensional Dirichlet tube. Helv. Phys. Acta, 71 (2): 133–162, 1998.Google Scholar
[Don84] H., Donnelly. Eigenvalue estimates for certain noncompact manifolds. Michigan Math. J., 31 (3): 349–357, 1984.Google Scholar
[Gér93] C., Gérard. Distortion analyticity for N-particle Hamiltonians. Helv. Phys. Acta, 66 (2): 216–225, 1993.Google Scholar
[Gui89] L., Guillopé. Théorie spectrale de quelques variétés à bouts. Ann. Sci. École Norm. Sup. (4), 22 (1): 137–160, 1989.Google Scholar
[HS00] W., Hunziker and I. M., Sigal. The quantum N-body problem. J. Math. Phys., 41 (6): 3448–3510, 2000.Google Scholar
[Hus05] R., Husseini. Zur spektraltheorie verallgemeinerter laplace-operatoren auf mannigfaltigkeiten mit zylindrischen enden. Diplomarbeit, Rheinischen Friedrich-Wilhelms-Universität Bonn, 2005.
[Kal10] V., Kalvin. The aguilar-baslev-combes theorem for the laplacian on a manifold with an axial analytic asymptotically cylindrical end. arXiv:10032538v2, 2010.
[KS07] H., Kovařík and A., Sacchetti. Resonances in twisted quantum waveguides. J. Phys.A, 40 (29): 8371–8384, 2007.Google Scholar
[Mül83] W., Müller. Spectral theory for Riemannian manifolds with cusps and a related trace formula. Math. Nachr., 111 : 197–288, 1983.Google Scholar
[Mül96] Werner, Müller. On the L2-index of Dirac operators on manifolds with corners of codimension two. I. J. Diff. Geom., 44 (1): 97–177, 1996.Google Scholar
[MV02] R., Mazzeo and A., Vasy. Resolvents and Martin boundaries of product spaces. Geom. Funct. Anal., 12 (5): 1018–1079, 2002.Google Scholar
[MV04] R., Mazzeo and A., Vasy. Analytic continuation of the resolvent of the Laplacian on SL(3)/SO(3). Amer. J. Math., 126 (4): 821–844, 2004.Google Scholar
[MV07] R., Mazzeo and A., Vasy. Scattering theory on SL(3)/SO(3): connections with quantum 3-body scattering. Proc. Lond. Math. Soc. (3), 94 (3): 545–593, 2007.Google Scholar
[Ros97] Steven, Rosenberg. The Laplacian on a Riemannian manifold, London Mathematical Society Student Texts 31. Cambridge: Cambridge University Press, 1997.
[RS79] M., Reed and B., Simon. Methods of modern mathematical physics. III. New York: Academic Press, 1979.
[RS80] M., Reed and B., Simon. Methods of modern mathematical physics. I, 2nd edn. New York: Academic Press, 1980.
[Shu91] M. A., Shubin. Spectral theory of elliptic operators on non-compact manifolds. Paper presented at the Summer School on Semiclassical Methods, Nantes, 1991.
[SZ93a] J., Sjöstrand and M., Zworski. Estimates on the number of scattering poles near the real axis for strictly convex obstacles. Ann. Inst. Fourier (Grenoble), 43 (3): 769–790, 1993.Google Scholar
[SZ93b] J., Sjöstrand and M., Zworski. Lower bounds on the number of scattering poles. Comm. Partial Diff. Equations, 18 (5–6): 847–857, 1993.Google Scholar
[SZ94] J., Sjöstrand and M., Zworski. Lower bounds on the number of scattering poles. II. J. Funct. Anal., 123 (2): 336–367, 1994.Google Scholar
[SZ95] J., Sjöstrand and M., Zworski. The complex scaling method for scattering by strictly convex obstacles. Ark. Mat., 33 (1): 135–172, 1995.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
×