Mean curvature rigidity of horospheres, hyperspheres and hyperplanes Rabah Souam

Rabah Souam

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arXiv · 1912.02669

Mean curvature rigidity of horospheres, hyperspheres and hyperplanes Rabah Souam

Rabah Souam

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Abstract

We prove that horospheres, hyperspheres and hyperplanes in a hyperbolic space H n , n $\ge$ 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 $\ge$ 0.

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Rabah Souam. 2019-12-05. Mean curvature rigidity of horospheres, hyperspheres and hyperplanes Rabah Souam. https://arxiv.org/abs/1912.02669

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