# Meromorphically normal families and a meromorphic Montel-Carath\'eodory theorem

## TL;DR

This paper establishes new sufficient conditions for meromorphic normality of families of mappings into projective space and proves a meromorphic version of the Montel-Carathéodory theorem, extending classical results to the meromorphic setting.

## Contribution

It introduces a general criterion for meromorphic normality influenced by Fujimoto's work and develops meromorphic analogues of recent results on normal families and the Montel-Carathéodory theorem.

## Key findings

- Provided sufficient conditions for meromorphic normality.
- Established a meromorphic version of the Montel-Carathéodory theorem.
- Extended classical normal family results to meromorphic mappings.

## Abstract

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. We also establish a meromorphic version of the Montel-Carath\'eodory theorem.