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arXiv · 2202.07527

Isobarycentric Inequalities

Shoni Gilboa·Pazit Haim-Kislev·Boaz Slomka
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Abstract

We prove the following isoperimetric type inequality: Given a finite absolutely continuous Borel measure on ${\mathbb R}^n$, halfspaces 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.

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Shoni Gilboa, Pazit Haim-Kislev, Boaz Slomka. 2022-02-15. Isobarycentric Inequalities. https://doi.org/10.1093/imrn%2Frnac191

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