%0 Journal Article
%T 完备黎曼曲面上亚纯函数的唯一性<br>Uniqueness of Meromorphic Functions on Complete Riemann Surfaces
%A 曹派
%J Pure Mathematics
%P 190-197
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.151022
%X 在本文中&#65292;我们讨论了开黎曼曲面<i>S</i>上亚纯函数的分担唯一性问题。设<img src=\"https://html.hanspub.org/file/1252689-rId8.svg?20250205124856\" >为曲面<i>S</i>上的亚纯函数&#65292;<img src=\"https://html.hanspub.org/file/1252689-rId10.svg?20250205124856\" >和<img src=\"https://html.hanspub.org/file/1252689-rId12.svg?20250205124856\" >为曲面<i>S</i>上的完备共形度量&#65292;<img src=\"https://html.hanspub.org/file/1252689-rId14.svg?20250205124856\" >为曲面<i>S</i>上的全纯1-形式。如果对于扩充复平面中不同的点<img src=\"https://html.hanspub.org/file/1252689-rId16.svg?20250205124856\" >有<img src=\"https://html.hanspub.org/file/1252689-rId18.svg?20250205124856\" >&#65292;<img src=\"https://html.hanspub.org/file/1252689-rId20.svg?20250205124856\" >且<img src=\"https://html.hanspub.org/file/1252689-rId22.svg?20250205124856\" >&#65292;则有<img src=\"https://html.hanspub.org/file/1252689-rId24.svg?20250205124856\" >。<br>In this paper, we discuss the uniqueness problem of meromorphic functions on an open Riemann surface. Let <img src=\"https://html.hanspub.org/file/1252689-rId26.svg?20250205124856\" > be meromorphic functions on the surface <i>S</i>, and <img src=\"https://html.hanspub.org/file/1252689-rId28.svg?20250205124856\" > and <img src=\"https://html.hanspub.org/file/1252689-rId30.svg?20250205124856\" > be two complete conformal metrics on the surface <i>S</i>, where <img src=\"https://html.hanspub.org/file/1252689-rId32.svg?20250205124856\" > are holomorphic 1-forms on the surface <i>S</i>. If there exists <img src=\"https://html.hanspub.org/file/1252689-rId34.svg?20250205124856\" > for different points <img src=\"https://html.hanspub.org/file/1252689-rId16.svg?20250205124856\" > in the expanded complex plane, <img src=\"https://html.hanspub.org/file/1252689-rId37.svg?20250205124856\" > and <img src=\"https://html.hanspub.org/file/1252689-rId22.svg?20250205124856\" >, then <img src=\"https://html.hanspub.org/file/1252689-rId40.svg?20250205124856\" >.
%K 黎曼曲面&#65292
%K 亚纯函数&#65292
%K 唯一性&#65292
%K 值分布<br>Riemann Surface
%K Meromorphic Function
%K Uniqueness
%K Value Distribution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=106259