Gradient estimates for a simple nonlinear heat equation on manifolds. Issue 2 (25th January 2017) - Ma, Li
Abstract : In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem on the compact Riemannian manifold ( M, g ) of dimension n and with non-negative Ricci curvature. Here is a constant, V is a smooth function on M with for some positive constant A . This heat equation is a basic evolution equation and it can be considered as the negative gradient heat flow to W -functional (introduced by G.Perelman), which is the Log-Sobolev inequalities on the Riemannian manifold and V corresponds to the scalar curvature.