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Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space

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  • Henrique F. de Lima
  • Joseilson R. de Lima

Abstract

We obtain a height estimate concerning to a compact spacelike hypersurface immersed with constant mean curvature in the anti-de Sitter space , when its boundary is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space . Our estimate depends only on the value of and on the geometry of As applications of our estimate, we obtain a characterization of hyperbolic domains of and nonexistence results in connection with such types of hypersurfaces.

Suggested Citation

  • Henrique F. de Lima & Joseilson R. de Lima, 2009. "Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-12, October.
    • Handle: RePEc:hin:jijmms:673508
    DOI: 10.1155/2009/673508
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