讲座题目：Isoparametric Submanifolds and Mean Curvature Flow

讲座时间：2021年6月28日，星期一，上午10:00—11:30

讲座地点：数学楼2-1会议室

讲座人：刘小博教授 ，北京大学

讲座摘要：

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 Chuu-Lian Terng and Marco Radeschi.

讲座人简介：

   北京大学讲席教授,北京国际数学研究中心副主任，北京大学数学研究所副所长。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. Journal等国际著名期刊上发表多篇高质量论文。