A Criterion for quasi normality in $\mathbb{C}^n$

TL;DR

This paper establishes a Zalcman type renormalization criterion to characterize quasi-normality of families of holomorphic functions in several complex variables, extending classical results to complex Hermitian manifolds.

Contribution

It introduces a new criterion for quasi-normality in several complex variables, generalizing existing one-variable results to functions taking values in Hermitian manifolds.

Findings

Provides a Zalcman type renormalization result for quasi-normality.

Extends classical quasi-normality criteria to higher dimensions.

Applies to families of holomorphic functions into Hermitian manifolds.

Abstract

In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in $\mathbb{C}^n$ that takes values in a complete complex Hermitian manifold.