Nevanlinna theory through the Brownian motion  

作　　者：Xianjing Dong Yan He Min Ru 

机构地区：[1]Department of Mathematics,Nanjing University,Nanjing 210093,China [2]Department of Mathematics,University of Houston,Houston,TX 77004,USA

出　　处：《Science China Mathematics》2019年第11期2131-2154,共24页中国科学：数学（英文版）

基　　金：supported by Simons Foundation (Grant No. 531604)

摘　　要：In this paper, we introduce the Nevanlinna theory using stochastic calculus, following the works of Davis(1975), Carne(1986) and Atsuji(1995, 2005, 2008 and 2017), etc. In particular, we give(another) proofs of the classical result of Nevanlinna for meromorphic functions and the result of Cartan-Ahlfors for holomorphic curves by using the probabilistic method.In this paper, we introduce the Nevanlinna theory using stochastic calculus, following the works of Davis(1975), Carne(1986) and Atsuji(1995, 2005, 2008 and 2017), etc. In particular, we give(another) proofs of the classical result of Nevanlinna for meromorphic functions and the result of Cartan-Ahlfors for holomorphic curves by using the probabilistic method.

关 键 词：NEVANLINNA theory HOLOMORPHIC CURVES second main THEOREM BROWNIAN motion 

分 类 号：O17[理学—数学]