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arXiv · 2410.21093

A Blaschke-Santal\'o inequality for unconditional log-concave measures

Emanuel Milman·Amir Yehudayoff
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Abstract

The Blaschke-Santal\'o inequality states that the volume product $|K| \cdot |K^{o}|$ of a symmetric convex body $K \subset \mathbb{R}^n$ is maximized by the standard Euclidean unit-ball. Cordero-Erausquin asked whether the inequality remains true for all even log-concave measures. We briefly survey the literature around this question and provide details for the known fact that the inequality holds true for all unconditional log-concave measures.

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BibTeXRIS

Emanuel Milman, Amir Yehudayoff. 2024-10-28. A Blaschke-Santal\'o inequality for unconditional log-concave measures. https://arxiv.org/abs/2410.21093

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