摘要：In this talk, I will first recall the entropy power inequalities for the heat equation and nonlinear diffusion equation (NLDE) on Euclidean spaces. Then I will present our recent results on the entropy power inequalities for the heat equation and nonlinear diffusion equation associated with the Laplace-Beltrami operator and the Witten Laplacian on Riemannian manifolds and Ricci flow.