报告题目：Mean curvature rigidity phenomenon and its extensions

报告人：马翔 教授 （北京大学）

时间：2025年4月25日 （星期五）上午10:00-11:00

地点：理科楼A404

摘要：A theorem by Gromov asserts that for a hyperplane in the Euclidean space E^n, any smooth perturbation with compact support and nonnegative mean curvature H must be trivial (i.e. identical to the original one). We will start by presenting Souam's simple proof of this rigidity result using the tangency principle. Then we consider similar problems for the unit (hyper-)sphere with mean curvature H=1 in E^n. Our main result says that when one perturbs the sphere only in a hemisphere, and the mean curvature H is no less than 1 for this smooth hypersurface after perturbation, then under quite natural conditions it must be congruent to the round sphere. On the other hand, if the fixed part of the sphere is only a small spherical cap, then there exist nontrivial perturbations on the complementary great spherical cap such that H is greater than 1 on the perturbed part. If time allowed, I will report further results and open problems in this direction. This is a joint work with Prof. Shibing CHEN (from USTC) and my previous student Shengyang WANG.

个人简介：马翔是北京大学数学科学学院教授。他师从王长平教授攻读研究生，后于2005年在柏林工业大学获得博士学位，导师为Ulrich Pinkall教授。其研究主要聚焦于子流形理论（包括极小曲面、Willmore曲面、莫比乌斯几何），尤其关注具有几何不变性且蕴含深刻几何直观的各类全局性问题。

邀请人：李海中，马辉，陈大广