Normal criteria for the family of meromorphic functions

Abstract

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 conditionson normal families of meromorphic functions. We also prove some normal conditions concerning domains by applyingAhlfors covering surfaces in this paper.