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- Title
Constant Mean Curvature Hypersurfaces in Anti-de Sitter Space.
- Authors
Trebeschi, Enrico
- Abstract
We study entire spacelike constant mean curvature hypersurfaces in Anti-de Sitter space of any dimension. First, we give a classification result with respect to their asymptotic boundary, namely we show that every admissible sphere |$\Lambda $| is the boundary of a unique such hypersurface, for any given value |$H$| of the mean curvature. We also demonstrate that, as |$H$| varies in |$\mathbb {R}$| , these hypersurfaces analytically foliate the invisible domain of |$\Lambda $|. Finally, we extend Cheng-Yau Theorem to the Anti-de Sitter space, which establishes the completeness of any entire constant mean curvature hypersurface.
- Subjects
CURVATURE; SPHERES; HYPERSURFACES; CLASSIFICATION
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 9, p8026
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnae032