Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature

In this paper we consider Riemannian manifolds of dimension at least 3, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we prove the validity of a new optimal Minkowski Inequality. Along with the proof, we establish sharp monotonicity formulas, holding along the level sets of p-capacitary potentials in p-nonparabolic manifolds with nonnegative Ricci curvature.