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arXiv · 1810.07507

Zhang's inequality for log-concave functions

David Alonso-Gutiérrez·Julio Bernués·Bernardo González Merino
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Abstract

Zhang's reverse affine isoperimetric inequality states that among all convex bodies $K\subseteq\mathbb{R}^n$, the affine invariant quantity $|K|^{n-1}|\Pi^*(K)|$ (where $\Pi^*(K)$ denotes the polar projection body of $K$) is minimized if and only if $K$ is a simplex. In this paper we prove an extension of Zhang's inequality in the setting of integrable log-concave functions, characterizing also the equality cases.

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David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino. 2018-10-17. Zhang's inequality for log-concave functions. https://arxiv.org/abs/1810.07507

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