Work

Mean curvature flow from conical singularities

Year: 2024

Type: article

Abstract: We prove Ilmanen’s resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface $M^{n}\subset \mathbb{R}^{n+1}$ Mn⊂Rn+1 , $2\leq n\leq 6$ 2≤n≤6 , with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens.

Source: Inventiones mathematicae

DOI: 10.1007/s00222-024-01296-8

Authors: Otis Chodosh, J. M. Daniels-Holgate, Felix Schulze

Institutions: Stanford University, Hebrew University of Jerusalem, 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

Funders: National Science Foundation, University of Warwick, European Commission