Self-similar shrinking solutions to mean curvature flow

Gergen Lecture #3

Simon Brendle (Columbia University)

Monday, November 21, 2016 -
4:00pm to 5:00pm
Physics 119

A key issue in the study of geometric flows is to understand singularity formation. Singularities are often modeled on self-similar solutions. Huisken and Colding-Minicozzi obtained a complete classification of all self-similar shrinking solutions to mean curvature flow with nonnegative mean curvature: the only examples are round spheres and cylinders. By contrast, there are many examples of self-similar shrinking solutions where the mean curvature changes sign. In this lecture, I will show that the sphere and cylinder are the only embedded self-similar shrinking solutions in R^3 of genus 0. This confirms conjectures of Brian White (in the compact case) and Tom Ilmanen (in the noncompact case).

Last updated: 2019/08/24 - 2:31pm