CHINA·77779193永利(集团)有限公司-Official website

李群与微分几何线上联合讨论班 

 题目：Isoparametric Submanifolds and Mean Curvature Flow 

报告人：刘小博 （北京大学） 

摘要：Ancient solutions are important in studying singularities of mean curvature flows (MCF). So far most rigidity results about ancient solutions are modeled on shrinking spheres or spherical caps. In this talk, I will describe the behavior of MCF for a class of submanifolds, called isoparametric submanifolds, which have more complicated topological type. We can show that all such solutions are in fact ancient solutions, i.e. they exist for all time which goes to negative infinity. Similar results also hold for MCF of regular leaves of polar foliations in simply connected symmetric spaces with non-negative curvature. I will also describe our conjectures proposed together with Terng on rigidity of ancient solutions to MCF for hypersurfaces in spheres. These conjectures are closely related to Chern’s conjecture for minimal hypersurfaces in spheres. This talk is based on joint works with ChuuLian Terng and Marco Radeschi.

报告人简介：北京大学讲席教授，北京国际数学研究中心副主任， 北京数学会理事长。曾任美国 University of Notre Dame 教 授，获得美国 Sloan 基金会 Research Fellowship，2006 年获 邀在马德里召开的国际数学家大会作 45 分钟报告。主要研究领 域包括Gromov-Witten不变量理论和等参子流形理论。在Annals of Mathematics, Duke Math. J.，Comm. Math. Phys., J. Diff. Geom 等国际著名期刊上发表多篇高质量论文。

报告时间：2022 年 11 月 16 日(周三) 19:30-21:00 

腾讯会议号：947-221-570 

欢迎全体师生积极参加!