Quantitative maximal diameter rigidity of positive Ricci curvature

报告人：任天寅 博士后（厦门大学）

时 间：2025年5月19日（星期一），上午9:30-10:30

地 点：海纳苑2幢202

摘 要：In Riemannian geometry, the Cheng’s maximal diameter rigidity theorem says that if a complete $n$-manifold $M$ of Ricci curvature, $\Ric_M \ge (n − 1)$, has the maximal diameter $\pi$, then $M$ is isometric to the unit sphere. The main result in this paper is a quantitative maximal diameter rigidity: if $M$ satisfies that $\Ric_M \ge n − 1$, $\diam(M) \approx \pi$, and the Riemannian universal cover of every metric ball in $M$ of a definite radius satisfies a Riefenberg condition, then $M$ is diffeomorphic and bi-H\older close to unit sphere, This work is a joint with Professor Xiaochun Rong.

联系人：江文帅（wsjiang@zju.edu.cn)