Rotational Symmetry of Mean Curvature Flows coming out of a double cone

Seminar: 
Geometric Analysis and Application
Event time: 
Friday, March 11, 2022 - 2:00pm
Speaker: 
Letian Chen
Speaker affiliation: 
Johns Hopkins University
Event description: 

Abstract:

We show that any initially smooth mean curvature flow (MCF) coming out of a rotationally symmetric double cone, which is singular at the origin, must stay rotationally symmetric for all time. Examples of such flows include (smooth) self-expanders, which are potential models of continuations of MCFs through conical singularities. I will also discuss non-self-similar, possibly singular, MCFs coming out of a cone that fit into our theorem