New Bernstein Type Results in Weighted Warped Products

Abstract

In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.

On Bernstein’s Problem of Complete Parabolic Hypersurfaces in Warped Products

“…Furthermore, [7] obtained uniqueness results for complete hypersurfaces in Riemannian warped products whose fiber has parabolic universal covering. More recently, by the weak Omori-Yau's maximum principle, the author [8] proved new Bernstein type results of complete constant weighted mean curvature hypersurfaces in weighted warped products I × ρ M n f . This paper is organized as follows: in Section 2, we introduce some basic facts for hypersurfaces in warped products.…”