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

Research output: Contribution to journalArticleScientificpeer-review


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

Research units

  • Shantou University
  • Hunan Normal University


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
Issue number1
Publication statusPublished - 1 Jan 2017
MoE publication typeA1 Journal article-refereed

    Research areas

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

ID: 9088541