报告人：胥世成 （首都师范大学）

时间：2021年12月10日 15:00

腾讯会议ID：233-725-793

摘要：Among the classical results in Riemannian geometry are the rigidity theorems, such as the Cheng's maximal diameter theorem and Bishop's maximal volume theorem, which says that if a Riemannian n-manifold M with Ricci curvature >=n-1 admits a maximal diameter or a maximal volume, then M is isometric to the standard sphere. In 1990s Cheeger-Colding and Perelman proved that the maximal volume rigidity actually is stable under a small perturbation on the volume. We prove that all space forms (not necessarily simply-connected) are also stable under a localized almost volume maximal condition. In particular, we prove a counterpart of Cheeger-Colding's almost maximal rigidty theorem for the case of the hyerbolic spaces, which states that if the universal cover of a closed Riemannian n-manifold M with Ricci curvature >=-(n-1) admits an almost maiximal exponential volume growth rate, then M is diffeomorphic to a hyperbolic space. This is a joint work with Prof. Xiaochun Rong and Lina Chen that was published in JDG recently.

个人简介：胥世成，首都师范大学数学科学学院副教授，研究方向为微分几何。主持国家自然科学基金创新群体子课题、面上项目等项目。在 JDG, Trans. Amer. Math. Soc. , Adv. Math., IMRN. 等杂志上发表多篇文章。