Geometric Analysis and Topology Seminar

New Results in Mean Curvature Flow in R^3

Speaker: Tom Ilmanen, ETH

Location: Warren Weaver Hall 512

Date: Friday, April 13, 2012, 11 a.m.


I will report on numerous new results for the evolution of surfaces by mean curvature flow in R^3, particularly when the density ratios are less than two. It includes a structure theorem for self-similar shrinking solutions, a monotonicity formula for self-expanding solutions, isolation of the cylinder, positive mean curvature in the neighborhood of a neckpinch, and progress toward the genericity conjecture for positive mean curvature singularities. (joint with Colding, Minicozzi, White)