Liouville theorem for the nonlinear Poisson equation on manifolds.

Abstract: In this note, we study a Modica type gradient estimate for smooth solutions to general non-linear Poisson equation where is a complete Riemannian manifold with bounded geometry and non-negative Ricci curvature and f is the derivative of the non-negative smooth function on R. Then we use this gradient estimate to conclude a Liouville theorem. [Copyright &y& Elsevier]