Dynamics of The Mean Curvature Flows

Speaker: Jinxin Xue (Tsinghua University)
Time & Date: 13:00, March 11
Location: Room 1710
Zoom Meeting ID: 423 317 8953 (Passcode: SIMIS)

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.