论某些域的双曲公设

IF 0.6 4区 数学 Q3 MATHEMATICS Computational Methods and Function Theory Pub Date : 2024-01-17 DOI:10.1007/s40315-023-00518-z
Aimo Hinkkanen, Matti Vuorinen
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引用次数: 0

摘要

我们证明,如果 E 是复平面上单位盘 \({{\mathbb {D}}}\) 的一个紧凑子集,如果 E 包含一系列不同点 \(a_n\not = 0\) for \(n\ge 1\) such that \(\lim _{n\rightarrow \infty } a_n=0\) and for all n we have \( |a_{n+1}| \ge |a_n|/2 \)、如果(G={{\mathbb {D}}} {\setminus } E\ )是连通的,并且(0\in \partial G\ ),那么有一个常数(c>;0),这样对于所有的(z在G中),我们都有\( \lambda _{G } (z)\ge c/(z) \ge c/|z| \) where \(\lambda _{G } (z)\) is the means of the G.(z)\) 是 G 中双曲度量的密度。
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On the Hyperbolic Metric of Certain Domains

We prove that if E is a compact subset of the unit disk \({{\mathbb {D}}}\) in the complex plane, if E contains a sequence of distinct points \(a_n\not = 0\) for \(n\ge 1\) such that \(\lim _{n\rightarrow \infty } a_n=0\) and for all n we have \( |a_{n+1}| \ge |a_n|/2 \), and if \(G={{\mathbb {D}}} {\setminus } E\) is connected and \(0\in \partial G\), then there is a constant \(c>0\) such that for all \(z\in G\) we have \( \lambda _{G } (z) \ge c/|z| \) where \(\lambda _{G } (z)\) is the density of the hyperbolic metric in G.

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来源期刊
Computational Methods and Function Theory
Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.20
自引率
0.00%
发文量
44
审稿时长
>12 weeks
期刊介绍: CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
期刊最新文献
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