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A geometric inequality and a low $M$-estimate

Author(s): Bo'az Klartag
Journal: Proc. Amer. Math. Soc. 132 (2004), 2619-2628.
MSC (2000): Primary 46B20, 52A20, 52A40
Posted: April 21, 2004
MathSciNet review: 2054787
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Abstract | References | Similar articles | Additional information

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: 10.1090/S0002-9939-04-07484-2
PII: S 0002-9939(04)07484-2
Keywords: Asymptotic geometric analysis, diameters of sections
Received by editor(s): May 26, 2003
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society




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