Mean curvature flows with cylindrical singularities II: stability and genericity

Abstract

In [SX25], we introduced the notion of nondegenerate cylindrical singularity using the ideas from dynamical systems. In this paper, we further study the properties of these singularities, showing that they are stable under small perturbations. Furthermore, we show that we can perturb some mean curvature flow with degenerate singularities to produce nondegenerate singularities.

arXiv comment30 Pages. This is the second part of ver 1 of https://arxiv.org/abs/2210.00419v1, with more details. Much progress has been made on this problem since 2022, and it is hard for us to keep track of it all; to reflect the original ideas in this work, we decided to keep our original references