Normal Families And Uniqueness Of Meromorphic Mappings In Several Complex Variables

In1925, Nevanlinna obtained two fundamental theorems about mero-morphic functions, which established the modern value distribution theory in one complex variable and has wide application in the uniqueness theory and normal family theory of meromorphic functions. And then, Cartan, Ahlfors, H. Weyl and F. Weyl study some related problems.Since1950s, Stoll and some other mathematicians had begun to study the value distribution theory in several complex variables. From then on, many famous mathematicians, such as Chern S. S., Griffiths P., Ru M., Siu Y.T., conducted deeply study in this topic. In1970s, Fojimoto studied the uniqueness theory and normal family theory of meromorphic mapping using value distribution theory in several complex variables and made a series of achievements. This paper will do related work in two aspects:one is to prove a necessary and sufficient condition for a holomorphic mapping family in several complex variables to be a normal family, and the other one is to improve and extend the uniqueness theory of meromorphic mapping in several complex variables. There are five chapters in this paper as follows:The first chapter introduces the history, status of value distribution theory, and outlines of our research work in the paper. The second chapter gives preliminary knowledge of the value distribution theory, including both respects for one complex variable and several complex variables. The third chapter deals with normal family theory of holomorphic mappings in several complex variables, and proves a necessary and sufficient condition for a family to be normal. The fourth chapter is concerned with uniqueness theorem of meromorphic mapping in several complex variables, and we prove two such theorems related to hyperplanes. The fifth chapter deals with uniqueness theorem related to moving hyperplanes, and we prove two extended and improved results.