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Pure Mathematics 2025
完备黎曼曲面上亚纯函数的唯一性
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Abstract:
在本文中，我们讨论了开黎曼曲面S上亚纯函数的分担唯一性问题。设![](\"https://html.hanspub.org/file/1252689-rId8.svg?20250205124856\")
为曲面S上的亚纯函数，![](\"https://html.hanspub.org/file/1252689-rId10.svg?20250205124856\")
和![](\"https://html.hanspub.org/file/1252689-rId12.svg?20250205124856\")
为曲面S上的完备共形度量，![](\"https://html.hanspub.org/file/1252689-rId14.svg?20250205124856\")
为曲面S上的全纯1-形式。如果对于扩充复平面中不同的点![](\"https://html.hanspub.org/file/1252689-rId16.svg?20250205124856\")
有![](\"https://html.hanspub.org/file/1252689-rId18.svg?20250205124856\")
，![](\"https://html.hanspub.org/file/1252689-rId20.svg?20250205124856\")
且![](\"https://html.hanspub.org/file/1252689-rId22.svg?20250205124856\")
，则有![](\"https://html.hanspub.org/file/1252689-rId24.svg?20250205124856\")
。
In this paper, we discuss the uniqueness problem of meromorphic functions on an open Riemann surface. Let ![](\"https://html.hanspub.org/file/1252689-rId26.svg?20250205124856\")
be meromorphic functions on the surface S, and ![](\"https://html.hanspub.org/file/1252689-rId28.svg?20250205124856\")
and ![](\"https://html.hanspub.org/file/1252689-rId30.svg?20250205124856\")
be two complete conformal metrics on the surface S, where ![](\"https://html.hanspub.org/file/1252689-rId32.svg?20250205124856\")
are holomorphic 1-forms on the surface S. If there exists ![](\"https://html.hanspub.org/file/1252689-rId34.svg?20250205124856\")
for different points in the expanded complex plane, ![](\"https://html.hanspub.org/file/1252689-rId37.svg?20250205124856\")
and , then ![](\"https://html.hanspub.org/file/1252689-rId40.svg?20250205124856\")
.
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