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

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

5 Scopus citations

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
State	Published - 1 Jan 2017
Externally published	Yes

Keywords

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

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10.1016/j.jmaa.2016.07.049

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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.",

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AU - Zhou, Qingshan

AU - Guan, Tiantian

AU - Huang, Manzi

AU - Rasila, Antti

PY - 2017/1/1

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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

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EP - 1119

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

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

Abstract

Keywords

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