Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, 58109-970, Paraíba, Brazil
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
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
As applications of our estimate, we obtain a characterization of hyperbolic domains of
and nonexistence results in connection with such types of hypersurfaces.