Advances in Mathematical Physics (Jan 2023)
On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products
Abstract
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.