Workshop on Geometric Functionals: Analysis and Applications

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.