An Application of Maximum Principle to space-like Hypersurfaces with Constant Mean Curvature in Anti-de Sitter Space

Details An Application of Maximum Principle to space-like Hypersurfaces with Constant Mean Curvature in Anti-de Sitter Space An Application of Maximum Principle to space-like Hypersurfaces with Constant Mean Curvature in Anti-de Sitter Space

2011-08-16

arxiv.org/abs/1108.3133v1

Mathematics

Differential Geometry

9 pages

Scientific paper

In this paper, we study complete hypersurfaces with constant mean curvature in anti-de Sitter space $H^{n+1}_1(-1)$. we prove that if a complete space-like hypersurface with constant mean curvature $x:\mathbf M\rightarrow H^{n+1}_1(-1) $ has two distinct principal curvatures $\lambda,\mu$, and inf$|\lambda-\mu|>0$, then $x$ is the standard embedding $ H^{m} (-\frac{1}{r^2})\times H^{n-m} (-\frac{1}{1 - r^2})$in anti-de Sitter space $ H^{n+1}_1 (-1)$.

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