English

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.

Keywords

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