An Alexandrov-type theorem in warped product manifolds with radial density

Abstract

In this paper, we establish a Heintze--Karcher inequality for closed embedded hypersurfaces in a class of warped product manifolds endowed with radial density. As a consequence, we prove Alexandrov-type theorem for constant weighted mean curvature hypersurfaces in such spaces. In particular, we prove that a closed embedded $λ$-self-expander in the Euclidean space must be a round sphere centered at the origin.