On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products - Ning Zhang; Zhangsheng Zhu (Advances in Mathematical Physics)
We study constant mean curvature hypersurfaces constructed over the fiber Mn of warped products I×fMn. In this setting, assuming that the sign of the angle function does not changed along the hypersurfaces, we infer the uniqueness of such hypersurfaces by applying a parabolicity criterion. As an application, we get some Bernstein type theorems.