Two-sided hypersurfaces, entire Killing graphs and the mean curvature equation in warped products with density

Abstract

In this paper, our purpose is to obtain uniqueness results related to the mean curvature equation for entire Killing graphs constructed over the base Pn of a warped product of the type Pfn×ρR with warping function ρ and density f. For this, we establish a suitable f-parabolicity criterion and, under appropriate constraints on the Bakry-Émery-Ricci tensor and on the f-mean curvature, we prove some rigidity results concerning two-sided hypersurfaces immersed in Pfn×ρR.