Universal Locally Univalent Functions and Universal Conformal Metrics with Constant Curvature

被引：2

作者：

Pohl, Daniel ^{[1
]}

Roth, Oliver ^{[1
]}

机构：

[1] Univ Wurzburg, Dept Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany

来源：

CONSTRUCTIVE APPROXIMATION | 2019年 / 50卷 / 01期

关键词：

Universal functions; Runge theory; Locally univalent functions; Conformal metrics; Constant curvature; HARMONIC-FUNCTIONS; THEOREM; APPROXIMATION;

D O I：

10.1007/s00365-018-9434-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M.Heins, we also show that there is a universal bounded locally univalent function on the unit disk. These results are used to prove that on any hyperbolic simply connected plane domain there exist universal conformal metrics with prescribed constant curvature.

引用

页码：145 / 165

页数：21

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