Meromorphically Normal Families in Several Variables

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.