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CHARACTERIZATION OF ELLIPSOIDS BY MEANS OF PARALLEL TRANSLATED SECTIONS

Part of:General convexity

Published online by Cambridge University Press:  13 July 2010

D. Larman,
L. Montejano and
E. Morales-Amaya
D. Larman
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K. (email: d.larman@math.ucl.ac.uk)
L. Montejano
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autonóma de México, Mexico (email: luis@matem.unam.mx)
E. Morales-Amaya
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autonóma de México, Mexico (email: efren@cimat.mx)

Abstract

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Let K be a convex body and let p0∈int K. Suppose that in every direction we can choose continuously a section of K which is a translated copy of the corresponding parallel section of K through p0. Our main result essentially claims that if all these pairs of sections are different almost everywhere, then K is an ellipsoid.

MSC classification

Secondary:52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)

Information

Type
Research Article
Information
Mathematika , Volume 56 , Issue 2 , July 2010, pp. 363 - 378
Copyright
Copyright © University College London 2010

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