报告人：任天寅博士

报告时间：2024年8月31日下午16:00-17:00

报告地点：理科综合楼105教室

报告题目：Quantitative maximal diameter rigidity of positive Ricci curvature

报告人简介：任天寅，厦门大学博士后，博士毕业首都师范大学。主要研究领域为度量黎曼几何。博士论文发表在J. Reine Angew(Crelle’s Journal)上。

报告摘要：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.