亚纯函数的正规定则 献给余家荣教授100华诞  

Normal criteria for the family of meromorphic functions

作　　者：孙道椿[1] 柴富杰 Daochun Sun;Fujie Chai

机构地区：[1]华南师范大学数学科学学院,广州510631 [2]广东金融学院金融数学与统计学学院,广州510521

出　　处：《中国科学：数学》2019年第11期1663-1674,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:111501127)资助项目

摘　　要：本文应用几何方法,深入研究亚纯函数的正规定则.首先定义并探讨球面上两点间的本性距离,在此基础上推广Montel正规定则和Marty正规定则,得到几个新的亚纯函数族正规的充要条件.本文还应用Ahlfors覆盖曲面理论,证明一些涉及区域的亚纯函数族的正规定则.In this paper, we investigate normal criteria of meromorphic functions deeply by using geometric methods. We first define and study the intrinsic distance between two points on the sphere. Then on this basis,we generalize Montel normal criterion and Marty normal criterion and obtain several sufficient and necessary conditions on normal families of meromorphic functions. We also prove some normal conditions concerning domains by applying Ahlfors covering surfaces in this paper.

关 键 词：亚纯函数 正规族 覆盖曲面 岛 限制域 

分 类 号：O1[理学—数学]