Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces

Ao Sun

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arXiv · 1810.08114

Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces

Ao Sun

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Abstract

In this paper we prove that the generic singularities of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modeled by closed self-shrinkers with multiplicity has multiplicity one. Together with the previous result by Colding-Minicozzi in [CM12], we conclude that the only generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modeled by closed self-shrinkers is a multiplicity one sphere. We also construct particular perturbations of the flow to avoid those singularities with multiplicity higher than one. Our result partially addresses the well-known multiplicity one conjecture by Ilmanen.

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Ao Sun. 2018-10-18. Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces. https://arxiv.org/abs/1810.08114

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