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Stability of neckpinch singularities

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arxiv 2006.06118 v2 pith:5FK6FZD3 submitted 2020-06-10 math.DG math.AP

Felix Schulze , Natasa Sesum This is my paper · ORCID
classification math.DGmath.AP
keywords singularitiesneckpinchstabilitycurvaturefirstflowmeanonly
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abstract

In this paper, we study the stability of neckpinch singularities. We show that if a mean curvature flow $\{M_t\}$ develops only finitely many neckpinch singularities at the first singular time, then the mean curvature flow starting at any sufficiently small perturbation of $M_0$ can also develop only neckpinch type singularities at the first singular time. We also show stability of nondegenerate neckpinch singularities in the above sense, which speaks in favor of stability of Type I singularities.

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