Work

The quermassintegral-preserving mean curvature flow in the sphere

Year: 2024

Type: article

Abstract: We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, starting from a strictly convex initial hypersurface, we prove that the flow exists for all times and converges smoothly to a geodesic sphere. This provides a workaround to an issue present in the volume preserving mean curvature flow in the sphere introduced by Huisken in 1987. We also classify solutions for some constant curvature type equations in space forms, as well as solitons in the sphere and in the upper branch of the De Sitter space.

Source: Analysis & PDE

DOI: 10.2140/apde.2024.17.3589

Authors: Esther Cabezas-Rivas, Julian Scheuer

Institutions: Universitat de València, Goethe University Frankfurt

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: European Regional Development Fund, Agencia Estatal de Investigación