论文标题
Nevanlinna理论通过全态形式
Nevanlinna theory via holomorphic forms
论文作者
论文摘要
本文重新开发了Nevanlinna理论，用于在holomorthic形式的角度上$ \ mathbb c $上的Meromorthic函数。根据我们的观察，nevanlinna的功能可以通过塑形形式提出。将这种想法应用于Riemann表面，然后使用holomorthic form $ \ mathscr s $扩展了Nevanlinna功能的定义。有了新的设置，获得了\ emph {弱$ \ mathscr s $ exexexed riemann表面的类似物，从而获得了$ \ Mathbb C $和$ \ Mathbb D. $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $
This paper re-develops the Nevanlinna theory for meromorphic functions on $\mathbb C$ in the viewpoint of holomorphic forms. According to our observation, Nevanlinna's functions can be formulated by a holomorphic form. Applying this thought to Riemann surfaces, one then extends the definition of Nevanlinna's functions using a holomorphic form $\mathscr S$. With the new settings, an analogue of Nevanlinna theory on \emph{weak $\mathscr S$-exhausted Riemann surfaces} is obtained, which is viewed as a generalization of the classical Nevanlinna theory on $\mathbb C$ and $\mathbb D.$
