Gradient estimates of Poisson equations on Riemannian manifolds and applications

Abstract: For the reflected diffusion generated by on a connected and complete Riemannian manifold M with empty or convex boundary, we establish some sharp estimates of of the Poisson equation in terms of the dimension, the diameter and the lower bound of curvature. Applications to transportation-information inequality, to Cheeger''s isoperimetric inequality and to Gaussian concentration inequality are given. Several examples are provided. [Copyright &y& Elsevier]