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arXiv · 2506.16941

Concavity principles for weighted marginals

Dario Cordero-Erausquin·Alexandros Eskenazis
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Abstract

We develop a general framework to study concavity properties of weighted marginals of $\beta$-concave functions on $\mathbb{R}^n$ via local methods. As a concrete implementation of our approach, we obtain a functional version of the dimensional Brunn-Minkowski inequality for rotationally invariant log-concave measures. Moreover, we derive a Pr\'ekopa-type concavity principle with rotationally invariant weights for even log-concave functions which encompasses the B-inequality.

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BibTeXRIS

Dario Cordero-Erausquin, Alexandros Eskenazis. 2025-06-20. Concavity principles for weighted marginals. https://arxiv.org/abs/2506.16941

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