Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space
We obtain a height estimate concerning to a compact spacelike hypersurface Σn immersed with constant mean curvature H in the anti-de Sitter space ℍ1n+1, when its boundary ∂Σ is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space ℍn. Our e...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/673508 |
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| Summary: | We obtain a height estimate concerning to a compact spacelike hypersurface Σn
immersed with constant mean curvature H
in the anti-de Sitter space ℍ1n+1, when its boundary ∂Σ
is contained into an umbilical spacelike hypersurface
of this spacetime which is isometric to the hyperbolic space ℍn. 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 ℍ1n+1
and nonexistence results in connection with such types of hypersurfaces. |
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| ISSN: | 0161-1712 1687-0425 |