Speaker: 薛金鑫教授，清华大学

Inviter: 中国科学院数学院学术报告会组委

Title: Dynamics of the mean curvature flows

Language: Chinese

Time & Venue: 2025.01.10 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: Mean curvature flow is to evolve an embedded hypersurface in Euclidean space according to the vector field given by the mean curvature at each point. We show how to extract geometric information from the asymptotics of a mean curvature flow approaching a singularity. We show that when the flow approaches a cylinder in a nondegenerate manner, i.e. with the slowest asymptotic rate, the flow can be extended through the singularity and the topology change can be described explicitly. When the flow approaches a cylinder in a degenerate manner, i.e. with exponential asymptotic rate, the singularity set can be proved to be at least C^2 modulo a lower dimensional set.This talk is based on a series of works jointly with Ao Sun and Zhihan Wang.