A note on exhaustion of hyperbolic complex manifolds

The purpose of this article is to investigate a hyperbolic complex manifold $M$ exhausted by a pseudoconvex domain $Ω$ in $\mathbb C^n$ via an exhausting sequence $\{f_j\colon Ω\to M\}$ such that $f_j^{-1}(a)$ converges to a boundary point $ξ_0 \in \partial Ω$ for some point $a\in M$.

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