Improvements to the Montel-Carath\'eodory Theorem for families of $\mathbb{P}^n$-valued holomorphic curves

Abstract

In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain $D\subseteq\mathbb{C}$ into $\mathbb{P}^n$ to be normal. Our results are improvements to the Montel-Carath\'eodory Theorem for a family of $\mathbb{P}^n$-valued holomorphic curves.