Bifurcation of perturbations of non-generic closed self-shrinkers

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.

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