Ahlfors' currents in higher dimension

TL;DR

This paper establishes criteria for constructing Ahlfors' currents in higher-dimensional compact hermitian manifolds using nondegenerate holomorphic maps from complex manifolds.

Contribution

It introduces new criteria for constructing Ahlfors' currents in higher dimensions, extending previous methods to more complex geometric settings.

Findings

Criteria for constructing Ahlfors' currents in higher dimensions

Extension of Ahlfors' currents to compact hermitian manifolds

Application to nondegenerate holomorphic maps

Abstract

We consider a nondegenerate holomorphic map $f: V \mapsto X$ where $(X, \omega)$ is a compact hermitian manifold of dimension higher or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$. In this article we give criteria which permit to construct Ahlfors' currents in $X$.