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 Lp-Euclidean Nash inequality and Lp-Euclidean Logarithmic Sobolev inequality, moreover, an improvement of Lp-Logarithmic Sobolev inequality is derived.