We give conditions in order to approximate locally uniformly holomorphic covering mappings of the unit ball of \({{\mathbb {C}}^{n}}\) with respect to an arbitrary norm, with entire holomorphic covering mappings. The results rely on a generalization of the Loewner theory for covering mappings which we develop in the paper.

中文翻译：

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全纯覆盖图的逼近和Loewner理论

我们给出条件以相对于任意范数近似逼近\（{{\ mathbb {C}} ^ {n}} \）的单位球的局部均匀全纯覆盖映射，以及整个全纯覆盖映射。结果依赖于Loewner理论的概括来覆盖我们在本文中开发的映射。