Distortion of quasiconformal maps in terms of the quasihyperbolic metric

被引：7

作者：

Soultanis, Elefterios ^{[1
]}

Williams, Marshall ^{[2
]}

机构：

[1] Univ Helsinki, FI-00014 Helsinki, Finland

[2] Univ Jyvaskyla, Dept Math, Jyvaskyla 40014, Finland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 402卷 / 02期

基金：

芬兰科学院;

关键词：

Metric measure spaces; Spaces of Q-bounded geometry; Quasiconformal maps; Quasihyperbolic metric;

D O I：

10.1016/j.jmaa.2013.01.061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend a theorem of Gehring and Osgood from 1979 - relating to the distortion of the quasihyperbolic metric by a quasiconformal mapping between Euclidean domains - to the setting of metric measure spaces of Q-bounded geometry. When the underlying target space is bounded, we require that the boundary of the image has at least two points. We show that even in the manifold setting, this additional assumption is necessary. (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：626 / 634

页数：9

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