Isobarycentric Inequalities

Author:

Gilboa Shoni1,Haim-Kislev Pazit2,Slomka Boaz A1

Affiliation:

1. Department of Mathematics, The Open University of Israel , Raanana 4353701, Israel

2. Department of Mathematics, Tel Aviv University , Tel Aviv 6997801, Israel

Abstract

Abstract We prove the following isoperimetric-type inequality: Given a finite absolutely continuous Borel measure on ${\mathbb {R}}^n$, half-spaces have maximal measure among all subsets with prescribed barycenter. As a consequence, we make progress towards a solution to a problem of Henk and Pollehn, which is equivalent to a log-Minkowski inequality for a parallelotope and a centered convex body. Our probabilistic approach to the problem also gives rise to several inequalities and conjectures concerning the truncated mean of certain log-concave random variables.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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