The concavity of p-entropy power and applications in functional inequalities

In this paper, we prove the concavity of p-entropy power of probability densities solving the p-heat equation on closed Riemannian manifold with nonnegative Ricci curvature. As applications, we give new proofs of L-p-Euclidean Nash inequality and L-p-Euclidean Logarithmic Sobolev inequality, moreover, an improvement of L-p-Logarithmic Sobolev inequality is derived. (C) 2018 Elsevier Ltd. All rights reserved.