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- Title
Mean curvature flow with generic initial data.
- Authors
Chodosh, Otis; Choi, Kyeongsu; Mantoulidis, Christos; Schulze, Felix
- Abstract
We show that the mean curvature flow of generic closed surfaces in 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 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.
- Subjects
CURVATURE; HYPERSURFACES; SOLITONS
- Publication
Inventiones Mathematicae, 2024, Vol 237, Issue 1, p121
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-024-01258-0