Year: 2022
Type: article
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.
DOI: 10.1093/imrn/rnac191
Authors: Shoni Gilboa, Pazit Haim-Kislev, Boaz A Slomka
Institutions: Open University of Israel, Tel Aviv University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226231950