A Blaschke-Santaló inequality for unconditional log-concave measures

Abstract

The Blaschke-Santaló 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.

9 pages, to appear in Ann. Fac. Sci. Toulouse Math