Genus one singularities in mean curvature flow
数学专题报告
报告题目(Title)：Genus one singularities in mean curvature flow
报告人(Speaker)：Ao Sun (Lehigh University)
地点(Place)：ZoomID: 968 7788 7622 密码: 107767
时间(Time)：2023 年 10月 20日09：30—10：30
邀请人(Inviter)：熊金钢
报告摘要
We show that for certain one-parameter families of initial conditions in ℝ³, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts sharply with the case of just a single flow. Among applications, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut, and we proved that the fourth lowest entropy self-shrinker in ℝ³ can not be rotationally symmetric. Based on joint work with Adrian Chu.
* This PDE seminar is co-organized with Tianling Jin at The Hong Kong University of Science and Technology. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
