Bifurcation of perturbations of non-generic closed self-shrinkers
Differential Geometry
2020-12-09 v3
Abstract
We discover a bifurcation of the perturbations of non-generic closed self-shrinkers. If the generic perturbation is outward, then the next mean curvature flow singularity is cylindrical and collapsing from outside; if the generic perturbation is inward, then the next mean curvature flow singularity is cylindrical and collapsing from inside.
Cite
@article{arxiv.2004.07787,
title = {Bifurcation of perturbations of non-generic closed self-shrinkers},
author = {Zhengjiang Lin and Ao Sun},
journal= {arXiv preprint arXiv:2004.07787},
year = {2020}
}
Comments
21 pages, 1 figures; We rewrite our proof of theorem 3.1 about the finite time singularity in this version. To appear in Journal of Topology and Analysis