Computational Methods and Function Theory ( IF 2.1 ) Pub Date : 2021-08-24 , DOI: 10.1007/s40315-021-00413-5 Gopal Datt 1
In this paper, we present various sufficient conditions for a family of meromorphic mappings on a domain \(D\subset {\mathbb {C}}^m\) into \({\mathbb {P}}^n\) to be meromorphically normal. Meromorphic normality is a notion of sequential compactness in the meromorphic category introduced by Fujimoto. We give a general condition for meromorphic normality that is influenced by Fujimoto’s work. The approach to proving this result allows us to establish meromorphic analogues of several recent results on normal families of \({\mathbb {P}}^n\)-valued holomorphic mappings.
中文翻译:
几个变量中的亚纯正态族
在本文中,我们为家庭域上亚纯映射的本各个充分条件\(d \子集{\ mathbb {C}} ^ M \)到\({\ mathbb {P}} ^ N \)是亚形正常。亚纯正态性是 Fujimoto 引入的亚纯范畴中顺序紧致的概念。我们给出了受藤本工作影响的亚纯正态性的一般条件。证明这个结果的方法允许我们在\({\mathbb {P}}^n\)值全纯映射的正常族上建立几个最近结果的亚纯类似物。