Mean curvature flow with generic initial data

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 technica...

Full description

Saved in:
Bibliographic Details
Published in:Inventiones mathematicae 2024-07, Vol.237 (1), p.121-220
Main Authors: Chodosh, Otis, Choi, Kyeongsu, Mantoulidis, Christos, Schulze, Felix
Format: Article
Language:English
Subjects:
Asymptotic properties
Curvature
Entropy
Hyperspaces
Mathematics
Mathematics and Statistics
Solitary waves
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-024-01258-0