Compact spacelike hypersurfaces with constant mean curvature in the anti de Sitter space
type: Item
instance of: scholarly article
title: Compact spacelike hypersurfaces with constant mean curvature in the anti de Sitter space
zbMATH Open document ID: 1178.83006
DOI: 10.1155/2009/673508
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45735
review text: Summary: We obtain a height estimate concerning to a compact spacelike hypersurface \(\Sigma ^{n}\) immersed with constant mean curvature \(H\) in the anti-de Sitter space \(\mathbb H_{1}^{n+1}\), when its boundary \(\partial\Sigma \) is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space \(\mathbb H^{n}\). Our estimate depends only on the value of \(H\) and on the geometry of \(\partial \Sigma\). As applications of our estimate, we obtain a characterization of hyperbolic domains of \(\mathbb H_{1}^{n+1}\) and nonexistence results in connection with such types of hypersurfaces.
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 5627901
Wikidata QID: Q58648496
author: Henrique Fernandes de Lima
author: Joseílson R. De Lima
MaRDI profile type: Publication
OpenAlex ID: W2083729882
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description: scientific article; zbMATH DE number 5627901