Abstract
In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $\mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ \Delta ^n \setminus Z $ into $ X $, where $ Z $ is an analytic subset of $\Delta^n $ such that codimension of $ Z $ at least 2.
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