Differential Harnack estimates for parabolic equations

Abstract

Let (M,g(t)) be a solution to the Ricci flow on a closed Riemannian manifold. In this paper, we prove differential Harnack inequalities for positive solutions of nonlinear parabolic equations of the type (Formula presented.) We also comment on an earlier result of the first author on positive solutions of the conjugate heat equation under the Ricci flow. © Springer-Verlag Berlin Heidelberg 2011.