Isobarycentric Inequalities

Shoni Gilboa*, Pazit Haim-Kislev, Boaz A. Slomka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove the following isoperimetric-type inequality: Given a finite absolutely continuous Borel measure on, 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.

Original languageEnglish
Pages (from-to)12298-12323
Number of pages26
JournalInternational Mathematics Research Notices
Issue number14
StatePublished - 1 Jul 2023


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