Self-similar solutions of mean curvature flow and entropy

Workshop on Geometric Functionals: Analysis and Applications
Topic:Self-similar solutions of mean curvature flow and entropy
Speaker:Jacob Bernstein
Affiliation:Johns Hopkins University; Member, School of Mathematics
Date:Monday, March 4
Time/Room:2:30pm - 3:30pm/Simonyi Hall 101

Abstract: Colding-Minicozzi introduced a natural entropy for hypersurfaces in euclidean space that is non-increasing under the mean curvature flow (MCF) and is a natural measure of the hypersurface's geometric complexity.  In particular, hypersurfaces of low entropy turn out to be "simple" in various senses.  This phenomena is most striking for self-similar solutions of MCF and I will discuss recent results illustrating this.  This is all joint work with Lu Wang.