报告人：胥世成，首都师范大学，副教授

Title：Convergence, Rigidity and Stability Theorems in Riemannian Geometry

Abstract：The rigidity of special manifolds such as space forms is one of classical problems in Riemannian Geometry. For example, if Ricci curvature of a Riemannian manifold (M,g) is no less than (n-1), then the diameter of M is no bigger than \pi. Cheng’s maximal diameter theorem says that if diameter of M equals to \pi, then (M,g) is isometric to the standard unit sphere. It is natural to ask stability problem in the sense that if the diameter of M close to \pi under same curvature condition, then would M close to the standard sphere? This closeness can be formulated rigorous in Gromov-Hausdorff distance, which is a kind of distance between metric space. Moreover, just as real numbers, one may consider a converging sequence of manifolds to find geometric/topological relationship between them. Such idea has provided powerful tools in the study of Riemannian manifolds, including rigidity and stabilty problems mentioned above. Basic tools and ideas of such convergence as well as very recent related progress on stablity problem will be introduced in this talk.

时间：2016年12月6日（星期二）下午3：00-4：00，

地点：知新楼B座1032