A note on exhaustion of hyperbolic complex manifolds

Abstract

The purpose of this article is to investigate a hyperbolic complex manifold $M$ exhausted by a pseudoconvex domain $\Omega$ in ${\mathbb{C}}^n$ via an exhausting sequence $\{f_j:\Omega \to M\}$ such that $f_j^{-1}(a)$ converges to a boundary point ${\xi }_0\in \partial \Omega$ for some point $a\in M$.

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