Value Distribution Theory Of Meromorphic Function And Circlr Packing Theory

In this thesis we mainly study value distribution theory of meromorphic function and circlr packing theory. This thesis is divided into four chapters.In chapter 1, we state some basic knowledge on value distribution theory and some classical theorems which will be used in the thesis.Let F be a family of functions meromorphic in a domain D (?)C F is said to be normal in D, if every sequence f_n∈ F contains a subsequence f_nk which converges to a meromorphic function f or identically ∞ spherically and locally uniformly in D.In chaper 2, we study normal families. In the theory of normal family, it is an important subject obtaining new normal criterion. In this chapter, we obtain some new normal criteria. This chapter is divided into four sections.In sections 2.1-2.2, we give some basic knowledge on normal family and some known results. In the theory of normal families before 1975, the usual methods was to found firstly a inequation about the characteristic function, then to expunction the original value. But Zalcman inaugurated a new approach. He established a sufficient and necessary condition about a family of meromorphic function being not normal based on the Marty normal criterion. We usually call it Zalcman Lemann. In section 2.3, we introduce in detail the method of Zalcman and its development.In section 2.4, we improve some normal criteria. The main difficulty in the proof is that how to prove the family of meromorphic function being normal at the zero of the analytic function when a complex constant is replaced a analytic function. By applying diversified methods in the theory of normal family, we...