Mean curvature rigidity of horospheres, hyperspheres and hyperplanes Rabah Souam

2019/12/05 by Rabah Souam, Souam, Rabah
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1912.02669

openalex publication_date 2019/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that horospheres, hyperspheres and hyperplanes in a hyperbolic space H n , n ≥ 3, admit no perturbations with compact support which increase their mean curvature. is is an extension of the analogous result in the Euclidean spaces, due to M. Gromov, which states that a hyperplane in a Euclidean space R n admits no compactly supported perturbations having mean curvature ≥ 0.

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