The Uniqueness Problem For Meromorphic Mappings And Meromorphic Functions In Several Complex Variables

This thesis deals with the uniqueness problems with unique range sets for nonconstant function on Cm and the uniqueness problems of meromorphic mappings sharing hyperplanes and sharing moving targets,we obtain some uniqueness theorems which improve and extend the earlier work. The whole thesis consists of six chapters:In Chapter1,we introduce the general background of Nevanlinna Theory and review the development of uniqueness theory for meromorphic mappings in several complex.In Chapter2, using the properties of meromorphic functions on Cm (including Nevanlinna theory),we discuss the problems of unique range set for meromorphic functions on Cm,and we obtaion a result, which improves a result of Hu-Li-Yang. Also,we prove another related result.In Chapter3,for the uniqueness theorems of linearly nondegenerate meromorphic mappings sharing hyperplanes Lii and Tu-Wang studied independently, We take the idea dim(f-1(∩k+1j=1Hij))≤m-2(1≤i1＜…＜ik+1≤q)due to Giang-Quynh-Quang into consideration, and obtain corresponding new uniqueness theorems.In Chapter4,we study the uniqueness problem of linearly nondegenerate meromorphic mappings sharing moving targets,and we obtain a result, which extends Lii’s result.However, in Chapter5,without the assumption on the nondegeneracy, and consider multiple value, we also obtain two uniqueness theorems of meromorphic mappings "partially" sharing moving targets.In the last Chapter, we make a simple summary about the thesis.