Results On Value Distribution Theory Of Holomorphic Maps And Subharmonic Functions

The content of this thesis is divided into two parts:the first part is to study subharmonic functionsu（x）inBL（H,R）（28）{x（?）（49）^m:H（27）x（27）R,0（27）H（27）1（27）R},it could obtain a sharp inequality connecting betweenN（h,r;u）andB（h,r;u）,and a sharp bound ford（u）when there exists a₀h such that the orderlof the subharmonic function u is less than one inBL（H,R）;In the second part by introducting the current of sub-harmonic functions on the annuli,the characteristic function of holomorphic maps,and the Annulus’version of the Green-Jensen’s formula,we mainly obtain the second main theorm for holomorphic maps from annuli into compact Riemann surface.The thesis organized as follow:In chapter 1:Describe the research background of this dissertation,introduces some achievements of Nevanlinna theory and these main works of this dissertation.In chapter 2:Introduce some value distribution properties about subharmonic functions and then used to extend it.For example,the boundary of deficiency of subharmonic functions in BL（H,R）.In chapter 3:Introduce the establishing of the characteristic function and First Fundamental Theorem,and the proving of Second Fundamental Theorem.