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A geometric inequality and a low $M$-estimate


Author: Bo'az Klartag
Journal: Proc. Amer. Math. Soc. 132 (2004), 2619-2628
MSC (2000): Primary 46B20, 52A20, 52A40
DOI: https://doi.org/10.1090/S0002-9939-04-07484-2
Published electronically: April 21, 2004
MathSciNet review: 2054787
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Abstract: 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.


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Additional Information

Bo'az Klartag
Affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
Email: klartagb@post.tau.ac.il

DOI: https://doi.org/10.1090/S0002-9939-04-07484-2
Keywords: Asymptotic geometric analysis, diameters of sections
Received by editor(s): May 26, 2003
Published electronically: April 21, 2004
Additional Notes: This research was partially supported by the Israel Science Foundation and by the Minkowski Center for Geometry
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society

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