$\vec{w}h\alpha\mathfrak{t}\;\; \forall\mathbb{R}\varepsilon\ldots$

mean curvature flow and its self-shrinkers?

Keita Kunikawa (Tohoku University)
2013/11/22, 16:00
FU Berlin, Arnimallee 6, at room SR 031
About what?

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.