International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 673508, 12 pages
Research Article

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

Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, 58109-970, Paraíba, Brazil

Received 8 July 2009; Accepted 6 October 2009

Academic Editor: Christian Corda

Copyright © 2009 Henrique F. de Lima and Joseilson R. de Lima. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain a height estimate concerning to a compact spacelike hypersurface Σn immersed with constant mean curvature H in the anti-de Sitter space 1n+1, when its boundary Σ is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space n. Our estimate depends only on the value of H and on the geometry of Σ. As applications of our estimate, we obtain a characterization of hyperbolic domains of 1n+1 and nonexistence results in connection with such types of hypersurfaces.