The many-body Blaschke-Santaló type inequality via optimal transport

Shibing Chen, Yuanyuan Li, Dongmeng Xi +1

Let $K_1,\dots ,K_k\subset {\mathbb{R}}^n$ be origin-symmetric measurable sets of finite volume such that \[ \sum_{1\le i<j\le k}\langle x_i,x_j\rangle\le \binom{k}{2}, \qquad \forall\…