Work

Colding–Minicozzi entropies in Cartan–Hadamard manifolds

Year: 2025

Type: article

Abstract: We introduce a family of functionals defined on the set of submanifolds of Cartan–Hadamard manifolds which generalize the Colding–Minicozzi entropy of submanifolds of Euclidean space. We show these functionals are monotone under mean curvature flow under natural conditions. As a consequence, we obtain sharp lower bounds on these entropies for certain closed hypersurfaces and observe a novel rigidity phenomenon.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0032

Authors: Jacob Bernstein, Arunima Bhattacharya

Institutions: Johns Hopkins University, University of North Carolina at Chapel Hill

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Hypersurfaces of Low Entropy and Mean Curvature Flow, Mean Curvature Flow and Singular Minimal Surfaces