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Convex bodies with almost all k-dimensional sections polytopes

Published online by Cambridge University Press:  24 October 2008

Leoni Dalla
Affiliation:
University College, London
D. G. Larman
Affiliation:
University College, London

Extract

It is a well-known result of V. L. Klee (2) that if a convex body K in En has all its k-dimensional sections as polytopes (k ≥ 2) then K is a polytope.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

(1)Besicovitch, A. S.On the existence of subsets of finite measure of sets of infinite measure. Indag. math. 14 (1954), 339–44.Google Scholar
(2)Klee, V. L.Some characterisations of convex polyhedra. Acta Math. 102 (1959), 79107.CrossRefGoogle Scholar
(3)Marstrand, J. M.Some fundamental geometrical properties of plane sets of fractional dimensions. Proc. London Math. Soc. (3) 4 (1954), 257302.CrossRefGoogle Scholar
(4)Marstrand, J. M.The dimension of Cartesian product sets. Proc. Cambridge Philos. Soc. 50 (1954), 198202.CrossRefGoogle Scholar
(5)Mattila, P.Hausdorff dimension, orthogonal projections and intersections with planes. Annales Academiae Scientiarum Fennicae Series AI Mathematica 1 (1975), 227244.Google Scholar
(6)Schneider, R. Boundary structure and curvature of convex bodies. Proceeding of the conference in geometry,Siegen07 1978.CrossRefGoogle Scholar
(7)Schneider, R. Problem 3, ‘Konvexe Körper’. Oberwolfach 05 1978.Google Scholar