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The volume of the intersection of a convex body with its translates

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

M. Meyer ,
S. Reisner  and
M. Schmuckenschläger
M. Meyer
Affiliation:
Equipe d'Analyse, Université paris VI, F-75252-Paris, Cedex 05, France
S. Reisner
Affiliation:
Department of Mathematics, University of Haifa, Haifa, 31905, Israel
M. Schmuckenschläger
Affiliation:
Dept. Theoretical Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel
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Abstract

It is proved that for a symmetric convex body K in ℝn, if for some τ >0, |K ⋂ (x + τK) depends on ‖x‖K only, then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies are studied.

MSC classification

Secondary: 52A38: Length, area, volume
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 278 - 289
Copyright
Copyright © University College London 1993

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