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arXiv · 2201.02360

Nevanlinna theory via holomorphic forms

Xianjing Dong·Shuangshuang Yang
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Abstract

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 $\mathbb D.$

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Xianjing Dong, Shuangshuang Yang. 2022-01-07. Nevanlinna theory via holomorphic forms. https://doi.org/10.2140/pjm.2022.319.55

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