We present an integral inequality connecting volumes and diameters of sections of a convex body. We apply this inequality to obtain some new inequalities concerning diameters of sections of convex bodies, among which is our "low M-estimate". Also, we give novel, alternative proofs to some known results, such as the fact that a finite volume ratio body has proportional sections that are isomorphic to a Euclidean ball.
Journal article
A geometric inequality and a low M-estimate
Proceedings of the American Mathematical Society, Vol.132(9), pp.2619-2628
Sep/2004
Abstract
Details
- Title
- A geometric inequality and a low M-estimate
- Creators
- Bo'Az Klartag (Corresponding Author) - Tel Aviv University
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.132(9), pp.2619-2628; Sep/2004
- Number of pages
- 10
- Language
- English
- DOI
- https://doi.org/10.1090/S0002-9939-04-07484-2
- Grant note
- Communicated by N. Tomcza. This research was partially supported by the Israel Science Foundation and by the Minkowski Center for Geometry. I would to thank V. Milman for encouraging me to write this paper and for hisvaluable suggestions during the research. Thanks also to M. Fradelizi for referringme to the paper.
- Record Identifier
- 993267332003596
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