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.
Reviewer: Wolfgang Weil (Karlsruhe)
MSC:
| 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 |
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