A note on the relationship between quasi-symmetric mappings and φ-uniform domains

Xiantao Wang; Qingshan Zhou; Tiantian Guan; Manzi Huang; Antti Rasila

doi:10.1016/j.jmaa.2016.07.049

A note on the relationship between quasi-symmetric mappings and φ-uniform domains

Xiantao Wang, Qingshan Zhou, Tiantian Guan, Manzi Huang, Antti Rasila^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

Abstract

The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,j_G)→(G,k_G) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.

Original language	English
Pages (from-to)	1114-1119
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	445
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.07.049
Publication status	Published - 1 Jan 2017
MoE publication type	A1 Journal article-refereed

Keywords

Distance ratio metric
Quasi-symmetric mapping
Quasihyperbolic metric
Uniform domain
φ-uniform domain

Access to Document

10.1016/j.jmaa.2016.07.049

Fingerprint Dive into the research topics of 'A note on the relationship between quasi-symmetric mappings and φ-uniform domains'. Together they form a unique fingerprint.

Cite this

@article{2abb8d4bfa504b7080cc649e4f5d4512,

title = "A note on the relationship between quasi-symmetric mappings and φ-uniform domains",

abstract = "The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,jG)→(G,kG) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by H{\"a}st{\"o}, Kl{\'e}n, Sahoo and Vuorinen, is negative.",

keywords = "Distance ratio metric, Quasi-symmetric mapping, Quasihyperbolic metric, Uniform domain, φ-uniform domain",

author = "Xiantao Wang and Qingshan Zhou and Tiantian Guan and Manzi Huang and Antti Rasila",

year = "2017",

month = jan,

day = "1",

doi = "10.1016/j.jmaa.2016.07.049",

language = "English",

volume = "445",

pages = "1114--1119",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - A note on the relationship between quasi-symmetric mappings and φ-uniform domains

AU - Wang, Xiantao

AU - Zhou, Qingshan

AU - Guan, Tiantian

AU - Huang, Manzi

AU - Rasila, Antti

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,jG)→(G,kG) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.

AB - The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,jG)→(G,kG) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.

KW - Distance ratio metric

KW - Quasi-symmetric mapping

KW - Quasihyperbolic metric

KW - Uniform domain

KW - φ-uniform domain

UR - http://www.scopus.com/inward/record.url?scp=84984806912&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.07.049

DO - 10.1016/j.jmaa.2016.07.049

M3 - Article

AN - SCOPUS:84984806912

VL - 445

SP - 1114

EP - 1119

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -