Compact spacelike hypersurfaces with constant mean curvature in the anti de Sitter space
Summary: We obtain a height estimate concerning to a compact spacelike hypersurface \(\Sigma ^{n}\) immersed with constant mean curvature \(H\) in the anti-de Sitter space \(\mathbb H_{1}^{n+1}\), when its boundary \(\partial\Sigma \) is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space \(\mathbb H^{n}\). Our estimate depends only on the value of \(H\) and on the geometry of \(\partial \Sigma\). As applications of our estimate, we obtain a characterization of hyperbolic domains of \(\mathbb H_{1}^{n+1}\) and nonexistence results in connection with such types of hypersurfaces.
scientific article; zbMATH DE number 5627901