A Bernstein type theorem in \(\mathbb R\times\mathbb H^n\)
Using the generalized Omori-Yau maximum principle, the authors prove the following theorem: Let \(\Sigma^n\) be a constant mean curvature, complete immersed hypersurface in \(\mathbb{R}\times \mathbb{H}^n\) such that the second fundamental form \(A\) is bounded. Assume that the angle function is bounded away from zero and that the height function \(h\) satisfies \(|\nabla h|^2\leq {\alpha\over n-1}|A|^2\) with some \(0<\alpha<1\). Then \(\Sigma^n\) is a slice in \(\mathbb{R}\times \mathbb{H}^n\).
scientific article; zbMATH DE number 6136412
scientific article