| In this paper, we study mainly about the application and generalization of the moving planes method. And the paper is composed of the following five parts.The first part is the prologue, in which we introduce the history of moving planes method, the applications and moving sphere method.The second part presents some preliminary knowledge which will be used in our study, such as the maximum theory, Hopf boundary point lemma.Then the moving planes method is introduced, and its use in a problem of symmetry of positive solution of elliptical partial differential equation.The fourth part is about our main result. In this part we present a new Harnack estimation of the problem of Ricci-Hamilton flow in S~2 sphere, which we get through the moving planes method.In the last part, we first introduce the Kelvin transform and the method of moving spheres , then introduce the existence and nonexistence of positive solutions of semilinear elliptical systems via the moving spheres method. |
