ABSTRACT

There have been many extensions of the Nevanlinna's five-values theorem for meromorphic functions to the case of meromorphic maps into ${\mathbb{P}}^n\left(\mathbb{C}\right).$ We improve these results by considering the degenerate case and using the weaker condition ‘$f^{-1}\left(H\right)\subseteq g^{-1}\left(H\right)$’ instead of the usual one ‘$f^{-1}\left(H\right)=g^{-1}\left(H\right)$’ for some hyperplanes H among the given hyperplanes. Our main theorems contain not only many well-known results but also more new conclusions. The sharpness of our results in some aspects is also explained.

中文翻译：

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ℂm到ℙn(ℂ)的亚纯映射唯一性定理的改进

摘要

亚纯函数的 Nevanlinna 的五值定理已经有许多扩展到亚纯映射到${\mathbb{磷}}^n\left(\mathbb{C}\right).$我们通过考虑退化情况并使用较弱的条件来改进这些结果$F^{-1}\left(H\right)\subseteq G^{-1}\left(H\right)$'而不是通常的'$F^{-1}\left(H\right)=G^{-1}\left(H\right)$' 对于给定超平面中的一些超平面H。我们的主要定理不仅包含许多众所周知的结果，而且还包含更多的新结论。我们的结果在某些方面的清晰度也得到了解释。