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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| Format: | Article |
| Language: | English |
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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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| author | Henrique F. de Lima Joseilson R. de Lima |
| author_facet | Henrique F. de Lima Joseilson R. de Lima |
| author_sort | Henrique F. de Lima |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-befd76b1759c4651a6463de1fa769d97 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-befd76b1759c4651a6463de1fa769d972025-02-03T01:02:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/673508673508Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter SpaceHenrique F. de Lima0Joseilson R. de Lima1Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, 58109-970, Paraíba, BrazilDepartamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, 58109-970, Paraíba, BrazilWe 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.http://dx.doi.org/10.1155/2009/673508 |
| spellingShingle | Henrique F. de Lima Joseilson R. de Lima Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space International Journal of Mathematics and Mathematical Sciences |
| title | Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space |
| title_full | Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space |
| title_fullStr | Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space |
| title_full_unstemmed | Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space |
| title_short | Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space |
| title_sort | compact spacelike hypersurfaces with constant mean curvature in the antide sitter space |
| url | http://dx.doi.org/10.1155/2009/673508 |
| work_keys_str_mv | AT henriquefdelima compactspacelikehypersurfaceswithconstantmeancurvatureintheantidesitterspace AT joseilsonrdelima compactspacelikehypersurfaceswithconstantmeancurvatureintheantidesitterspace |