An application of maximum principle to space-like hypersurfaces with constant mean curvature in anti-de Sitter space

摘要

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 ${x:mathbf Mrightarrow H^{n+1}_1(-1) }$ has two distinct principal curvatures λ, μ, and inf|λ − μ| 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 ${ H^{n+1}_1 (-1) }$ .