Geometric Analysis and Topology Seminar
Rigidity of Generic Singularities of Mean Curvature Flow
Speaker: Bill Minicozzi, MIT
Location: Warren Weaver Hall 517
Date: Friday, March 15, 2013, 11 a.m.
I will talk about joint work with Toby Colding and Tom Ilmanen on singularities of mean curvature flow (MCF). Self-shrinkers are special solutions that evolve by rescaling and model the singularities. There are infinitely many in each dimension, but the only generic are round cylinders. We prove that these are rigid in a very strong sense: Any other self-shrinker that is sufficiently close to one of them on a large, but compact, set must itself be a round cylinder. To our knowledge, this is the first general rigidity theorem for singularities of a nonlinear geometric flow. We expect that the techniques and ideas developed here have applications to other flows. Our results hold in all dimensions.