Gradient bounds and Liouville's type theorems for the Poisson equation on complete Riemannian manifolds (Q1908313)

The paper provides some nice gradient estimate and Liouville type theorems for the solutions of the Poisson equation on a complete manifold whose Ricci curvature is suitably restricted. The authors have remarked that methods related to those of the present paper have been used earlier by \textit{S.-Y. Cheng} [Proc. Symp. Pure Math., Vol. 36, 147-151 (1980; Zbl 0455.58009)], \textit{S.-Y. Cheng} and \textit{S.-T. Yau} [Commun. Pure Appl. Math. 28, 333-354 (1975; Zbl 0312.53031)] and the authors and \textit{L. Véron} [Duke Math. J. 74, No. 1, 223-236 (1994; Zbl 0813.53038)], to mention a few in order to derive a priori estimates in other geometric problems.