Some Research On Harnack Inequality On Surface Flow

In this paper,we study the inequality of a new nonlinear equation on the ?-Ricci flow based on the previous research.In addition,in the study of the relation between Entropy and Harnack inequality,based on the conjecture that there is a one-to-one correspondence between Entropy and Harnack inequality,we find an Entropy formula corresponding to the known Harnack on the Gauss curvature flow.This paper is mainly divided into the following three parts:1.We begin with a summary of some of the previous studies.2.We prove a new Harnack inequality for a nonlinear heat equation on ?-Ricci flow.3.We introduce and prove the existence of the Entropy formula corresponding to the known Harnack in the Gauss curvature flow.