Isobarycentric Inequalities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918087899480064 |
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| author | Gilboa, Shoni Haim-Kislev, Pazit Slomka, Boaz |
| author_facet | Gilboa, Shoni Haim-Kislev, Pazit Slomka, Boaz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07527 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Isobarycentric Inequalities Gilboa, Shoni Haim-Kislev, Pazit Slomka, Boaz Probability Metric Geometry 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. |
| title | Isobarycentric Inequalities |
| topic | Probability Metric Geometry |
| url | https://arxiv.org/abs/2202.07527 |