Sphericalization and flattening in quasi-metric measure spaces

被引:1
作者
Zhou, Qingshan [1 ]
Li, Xining [2 ]
Ponnusamy, Saminathan [3 ]
Li, Yaxiang [4 ]
机构
[1] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China
[2] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China
[3] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India
[4] Hunan First Normal Univ, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China
关键词
Quasi-metric spaces; Sphericalization; Flattening; Doubling condition; Ahlfors regular; Quasi-mobius; UNIFORM PERFECTNESS; GEOMETRY;
D O I
10.1016/j.jmaa.2022.126496
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The purpose of the note is to explore the invariance properties of sphericalization and flattening in quasi-metric spaces. We show that the Ahlfors regular and doubling property of quasi-metric spaces are preserved under sphericalization and flattening transformations. As an application, we give an improvement of a recent result in [21]. (c) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页数:23
相关论文
共 28 条
[11]  
Heinonen J., 2001, LECT ANAL METRIC SPA, DOI 10.1007/978-1-4613-0131-8
[12]   UNIFORMITY FROM GROMOV HYPERBOLICITY [J].
Herron, David ;
Shanmugalingam, Nageswari ;
Xie, Xiangdong .
ILLINOIS JOURNAL OF MATHEMATICS, 2008, 52 (04) :1065-1109
[13]  
Jarvi P, 1996, J LOND MATH SOC, V54, P515
[14]   Interplay between interior and boundary geometry in Gromov hyperbolic spaces [J].
Jordi, Julian .
GEOMETRIAE DEDICATA, 2010, 149 (01) :129-154
[15]  
Koblitz, 1984, GTM, V58
[16]   Preservation of Bounded Geometry under Sphericalization and Flattening [J].
Li, Xining ;
Shanmugalingam, Nageswari .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2015, 64 (05) :1303-1341
[17]   LIPSCHITZ FUNCTIONS ON SPACES OF HOMOGENEOUS TYPE [J].
MACIAS, RA ;
SEGOVIA, C .
ADVANCES IN MATHEMATICS, 1979, 33 (03) :257-270
[18]   METRIC CONFORMAL STRUCTURES AND HYPERBOLIC DIMENSION [J].
Mineyev, Igor .
CONFORMAL GEOMETRY AND DYNAMICS, 2007, 11 :137-163
[19]   QUASIMOBIUS MAPS [J].
VAISALA, J .
JOURNAL D ANALYSE MATHEMATIQUE, 1984, 44 :218-234
[20]  
Vellis V, 2021, Arxiv, DOI arXiv:1609.08763