Author:
Chodosh Otis,Choi Kyeongsu,Mantoulidis Christos,Schulze Felix
Abstract
AbstractWe show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$
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 $\mathbb{R}^{4}$
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.
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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