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A geometric inequality and a low \(M\)-estimate. (English) Zbl 1064.52003
Author’s 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.

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
46B20 Geometry and structure of normed linear spaces
52A40 Inequalities and extremum problems involving convexity in convex geometry
Full Text: DOI
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