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arXiv · 2003.14344

Mean curvature flow with generic initial data

Otis Chodosh·Kyeongsu Choi·Christos Mantoulidis·Felix Schulze
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Abstract

We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in $\mathbb{R}^{4}$ is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons.

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Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze. 2020-03-31. Mean curvature flow with generic initial data. https://arxiv.org/abs/2003.14344

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