2 research outputs found
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 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
Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space
We obtain a height estimate concerning to a compact spacelike hypersurface Σ n immersed with constant mean curvature H in the anti-de Sitter space H n 1 1 , when its boundary ∂Σ is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space H 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 H n 1 1 and nonexistence results in connection with such types of hypersurfaces