An extension of a theorem of Serrin to graphs in warped products (Q2577086)

Using a result of \textit{J. Serrin} [Philos. Trans. R. Soc. Lond., Ser. A 264, 413--496 (1969; Zbl 0181.38003)] on elliptic PDE, one can prove the existence and uniqueness of graphs of constant mean curvature in Euclidean space. In the paper under review, the authors extend this theorem to a wide class of Riemannian manifolds as ambient spaces. They use warped product representations which allow a natural notion of graph.