On the p-Renyi entropy power for nonlinear diffusion equations on Riemannian manifolds

Abstract

In this paper, we use a new method to prove the concavity of $p$-R\'enyi entropy power for doubly nonlinear diffusion equations on compact Riemanian manifolds with nonnegative Ricci curvature based on an explicit variational formula via trace free tensors. Moreover, we obtain the NIW formula between $p$-Renyi entropy power, $p$-Fisher information and $W$-entropy for doubly nonlinear diffusion equations.