Speaker：Zhefeng Xu (University of Science and Technology of China)

Time：2026-10-16 11: 00

Location：Conference Room S207 at Experiment Building at Haiyun Campus

Abstract:

Let $K_1,\ldots,K_k\subset\mathbb R^n$ be origin-symmetric measurable sets of finite volume such that $\sum_{1\le i<j\le k}\langle x_i,x_j\rangle\le \binom{k}{2}$, $\forall,x_i\in K_i,x_j\in K_j$. We prove the sharp many-body Blaschke--Santaló type inequality $\prod_{i=1}^k |K_i|\le |B^n|^k$ proposed by Kalantzopoulos and Saroglou, and characterize all equality cases. The proof combines multi-marginal optimal transport with a pseudo-Euclidean volume estimate. Using the geometric--functional equivalence of Kalantzopoulos and Saroglou, we also establish the functional version inequality proposed by Kolesnikov and Werner.