On the Entropies of Hypersurfaces with bounded mean curvature

2013/08/02 by Ilias, Said, Barbara Nelli, Nelli, Barbara +2
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1308.0628

openalex publication_date 2013/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in the impact of entropies on the geometry of a hypersurface of a Riemannian manifold. In fact, we will be able to compare the volume entropy of a hypersurface with that of the ambient manifold, provided some geometric assumption are satisfied. This depends on the existence of an embedded tube around such hypersurface. Among the consequences of our study of the entropies, we point out some new answers to a question of do Carmo on stable Euclidean hypersurfaces of constant mean curvature.

Citations

• Isoperimetric inequalities on minimal submanifolds of space forms

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