Exterior John Domains and Quasisymmetric Mappings

被引：0
|
作者：
Liu, Jinsong [1 ,2 ]
Xuan, Yi [1 ,2 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
COMPUTATIONAL METHODS AND FUNCTION THEORY | 2024年 / 24卷 / 01期
基金：
国家重点研发计划;
关键词：
John domains; Inner distances; Quasisymmetric mappings; Quasicomformal mappings;
D O I：
10.1007/s40315-023-00478-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we focus on exterior John domains. A John domain is called an exterior John domain if it is the exterior of a compact set. We prove that a quasiconformal mapping from the exterior of the closed unit ball to the exterior of a compact set is quasisymmetric with respect to the length inner distance if and only if its image is an exterior John domain. This result extends the classical results by N & auml;kki and V & auml;is & auml;l & auml; in R-2 (Expos Math 9:3-43, 1991, Thm. 7.4]) to arbitrary Euclidean space R-n.
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页码：7 / 25
页数：19
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