Geometric Analysis Seminar Nov 25, 2021: Jingxuan Zhang

In this and subsequent talks, we plan to disseminate a recent work on the stability of singularity of the mean curvature flow.

Abstract:

We study the rescaled mean curvature flow (MCF) of hypersurfaces that are global graphs over a fixed cylinder of arbitrary dimensions. We construct an explicit stable manifold for the rescaled MCF of finite codimensions in a suitable configuration space. For any initial hypersurface from this stable manifold, we construct a unique global solution to the rescaled MCF, and derive precise asymptotics for these solutions that are valid for all time. Using these asymptotics, we prove asymptotic stability of cylindrical singularities of arbitrary dimensions under generic initial perturbations.


Full paper online at https://arxiv.org/abs/2111.10111