Work

Mean curvature flow with generic initial data

Year: 2024

Type: article

Abstract: We 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.

Source: Inventiones mathematicae

DOI: 10.1007/s00222-024-01258-0

Authors: Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze

Institutions: Stanford University, Korea Institute for Advanced Study, Rice University, University of Warwick

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990