Gromov hyperbolicity in the free quasiworld. I

IF 0.7 3区 数学 Q2 MATHEMATICS
Qingshan Zhou, S. Ponnusamy
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引用次数: 5

Abstract

With the aid of a Gromov hyperbolic characterization of uniform domains, we first give an affirmative answer to an open question arisen by Väisälä under weaker assumption. Next, we show that the three-point condition introduced by Väisälä is necessary to obtain quasisymmetry for quasimöbius maps between bounded connected spaces in a quantitative way. Based on these two results, we investigate the boundary behavior of freely quasiconformal and quasihyperbolic mappings on uniform domains of Banach spaces and partially answer another question raised by Väisälä in different ways.
自由拟世界中的Gromov双曲性。我
借助于一致域的Gromov双曲刻画,我们首先在较弱的假设下对Väisälä提出的一个开放问题给出了肯定的答案。接下来,我们证明了Väisälä引入的三点条件对于在有界连通空间之间获得拟Möbius映射的拟对称性是必要的。基于这两个结果,我们研究了Banach空间一致域上自由拟共形和拟双曲映射的边界行为,并以不同的方式部分回答了Väisälä提出的另一个问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
期刊介绍: The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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