By applying Omori-Yau maximal principal theory and supposing an appropriate restriction on the norm of gradient of height function, we obtain some new Bernstein-type theorems for complete spacelike 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 spacetime and for hypersurfaces in hyperbolic space are given.
Yaning Wang. Ximin Liu. "On Complete Spacelike Hypersurfaces in a Semi-Riemannian Warped Product." J. Appl. Math. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/757041