On complete spacelike hypersurfaces in a semi-Riemannian warped product (Q2375661)

Summary: By applying the Omori-Yau maximum principle and supposing an appropriate restriction on the norm of the gradient of the height function, we obtain some new Bernstein-type theorems for complete space-like hypersurfaces with nonpositive constant mean curvature immersed in a semi-Riemannian warped product. Furthermore, some applications of our main theorems for entire vertical graphs in Robertson-Walker space-time and for hypersurfaces in hyperbolic space are given.