Free distance ratio mappings in Banach spaces

被引：3
作者：
Zhou, Qingshan [1 ]
Rasila, Antti [2 ]
Li, Yaxiang [3 ,4 ]
机构：
[1] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China
[2] Guangdong Technion Israel Inst Technol, 241 Daxue Rd, Shantou 515063, Guangdong, Peoples R China
[3] Hunan First Normal Univ, Dept Math, Changsha 410205, Hunan, Peoples R China
[4] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China
来源：
MONATSHEFTE FUR MATHEMATIK | 2020年 / 191卷 / 04期
关键词：
Quasihyperbolic metric; Distance ratio metric; Free distance ratio mapping; Free quasiconformal mapping; Uniform domains; FREE QUASICONFORMALITY; LIPSCHITZ-CONDITIONS; MAPS;
D O I：
10.1007/s00605-019-01337-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce a class of mappings related to the distance ratio metric and study its connection to the freely quasiconformal mapping in Banach spaces. Moreover, we investigate the invariance of Gromov hyperbolic, natural and uniform domains under this class of mappings.
引用
收藏
页码：843 / 856
页数：14
相关论文
共 24 条
[1]  
[Anonymous], 1988, LECT NOTES MATH
[2]   UNIFORM DOMAINS AND THE QUASI-HYPERBOLIC METRIC [J].
GEHRING, FW ;
OSGOOD, BG .
JOURNAL D ANALYSE MATHEMATIQUE, 1979, 36 :50-74
[3]   QUASI-CONFORMALLY HOMOGENEOUS DOMAINS [J].
GEHRING, FW ;
PALKA, BP .
JOURNAL D ANALYSE MATHEMATIQUE, 1976, 30 :172-199
[4]   INEQUALITIES AND BI-LIPSCHITZ CONDITIONS FOR THE TRIANGULAR RATIO METRIC [J].
Hariri, Parisa ;
Vuorinen, Matti ;
Zhang, Xiaohui .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2017, 47 (04) :1121-1148
[5]  
Hasto P.., 2016, J. Anal., V24, P57, DOI DOI 10.1007/S41478-016-0011-8
[6]   On quasisymmetry of quasiconformal mappings [J].
Huang, M. ;
Ponnusamy, S. ;
Rasila, A. ;
Wang, X. .
ADVANCES IN MATHEMATICS, 2016, 288 :1069-1096
[7]   Semisolidity and locally weak quasisymmetry of homeomorphisms in metric spaces [J].
Huang, Manzi ;
Rasila, Antti ;
Wang, Xiantao ;
Zhou, Qingshan .
STUDIA MATHEMATICA, 2018, 242 (03) :267-301
[8]   Lipschitz Continuity of Quasiconformal Mappings and of the Solutions to Second Order Elliptic PDE with Respect to the Distance Ratio Metric [J].
Li, Peijin ;
Ponnusamy, Saminthan .
COMPLEX ANALYSIS AND OPERATOR THEORY, 2018, 12 (08) :1991-2001
[9]   Apollonian metric, uniformity and Gromov hyperbolicity [J].
Li, Yaxiang ;
Vuorinen, Matti ;
Zhou, Qingshan .
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2020, 65 (02) :215-228
[10]   Weakly Quasisymmetric Maps and Uniform Spaces [J].
Li, Yaxiang ;
Vuorinen, Matti ;
Zhou, Qingshan .
COMPUTATIONAL METHODS AND FUNCTION THEORY, 2018, 18 (04) :689-715
123