具有非抛物线末端的完整 Kähler 连接和的 Nevanlinna 理论

Xianjing Dong
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引用次数: 0

摘要

在具有$\vartheta\geq2的连接和$\#^\vartheta\mathbb C^m$上的谐函数的Liouville性质无效性的激励下,我们研究了具有$\vartheta$非抛物线末端的完全K\"ahler连接和$$M=M_1\#\cdots\# M_\vartheta$$ 上的Nevanlinna理论。基于全局格林函数方法,我们将同态映射的第二个主要定理扩展到 $M.$。因此,在所有 $M_j^,s$ 都具有非负里奇曲率的条件下,我们得到了皮卡尔小定理,即如果 $M$ 上的每个同态函数省略了三个不同的值,那么它就会简化为一个常数。特别是,它意味着考奇-黎曼方程支持作为连通和下不变量的刘维尔性质的刚性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nevanlinna Theory on Complete Kähler Connected Sums With Non-parabolic Ends
Motivated by invalidness of Liouville property for harmonic functions on the connected sum $\#^\vartheta\mathbb C^m$ with $\vartheta\geq2,$ we study Nevanlinna theory on a complete K\"ahler connected sum $$M=M_1\#\cdots\# M_\vartheta$$ with $\vartheta$ non-parabolic ends. Based on the global Green function method, we extend the second main theorem of meromorphic mappings to $M.$ As a consequence, we obtain a Picard's little theorem provided that all $M_j^,s$ have non-negative Ricci curvature, which states that every meromorphic function on $M$ reduces to a constant if it omits three distinct values.In particular, it implies that Cauchy-Riemann equation supports a rigidity of Liouville property as an invariant under connected sums.
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