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 journalArticleScientificpeer-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,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.

Original languageEnglish
Pages (from-to)1114-1119
Number of pages6
JournalJournal of Mathematical Analysis and Applications
Volume445
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017
MoE publication typeA1 Journal article-refereed

Keywords

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

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