A geometric inequality and a low 𝑀-estimate

Klartag, Bo’az

doi:10.1090/S0002-9939-04-07484-2

A geometric inequality and a low $M$-estimate
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Proc. Amer. Math. Soc. 132 (2004), 2619-2628 Request permission

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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