On p-Brunn-Minkowski and Brascamp-Lieb inequalities
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| Format: | Preprint |
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2025
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| _version_ | 1866911435911593984 |
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| author | Kolesnikov, Alexander V. Livshyts, Galyna Rotem, Liran |
| author_facet | Kolesnikov, Alexander V. Livshyts, Galyna Rotem, Liran |
| contents | We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with $α$-homogeneous potential $V$ is equivalent to a $p$-Brunn--Minkowski inequality for level sets of $V$ with some $p(α,n)<0$. We establish links between several inequalities of this type on the sphere and the Euclidean space. Exploiting these observations, we prove new sufficient conditions for symmetric $p$-Brunn--Minkowski inequality with $p<1$. In particular, we prove the local log-Brunn--Minkowski for $L_q$-balls for all $q\geq 1$ in all dimensions, which was previously known only for $q\geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On p-Brunn-Minkowski and Brascamp-Lieb inequalities Kolesnikov, Alexander V. Livshyts, Galyna Rotem, Liran Functional Analysis We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with $α$-homogeneous potential $V$ is equivalent to a $p$-Brunn--Minkowski inequality for level sets of $V$ with some $p(α,n)<0$. We establish links between several inequalities of this type on the sphere and the Euclidean space. Exploiting these observations, we prove new sufficient conditions for symmetric $p$-Brunn--Minkowski inequality with $p<1$. In particular, we prove the local log-Brunn--Minkowski for $L_q$-balls for all $q\geq 1$ in all dimensions, which was previously known only for $q\geq 2$. |
| title | On p-Brunn-Minkowski and Brascamp-Lieb inequalities |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.12099 |