What is … mean curvature flow and their self-shrinkers?

This page hosts information on Keita Kunikawa's talk "What is … mean curvature flow and their self-shrinkers?" at the "What is …?" seminar. The talk will take place on Friday, November 22, 4:00pm at FU Arnimallee 6, SR 031.

Abstract

This talk is a short introduction to mean curvature flow (MCF). MCF is one of the geometric flows (PDE on manifolds). Start with a generic initial surface having singularities. After rescaling near a singularity, we can see a self-shrinker of the flow. They are special solutions of MCF and they do not change their shape under the flow (up to scaling). Classifying self-shrinkers is an important topic of research. In general, however, it is impossible to do so without some additional conditions. I will explain a method using the Gauss map to approach this problem.

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