Quasisymmetry and Quasihyperbolicity of Mappings on John Domains

Manzi Huang, Antti Rasila, Xiantao Wang*, Qingshan Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that G is a proper subdomain of Rn, f: G→ Y is a homeomorphism with a continuous extension to the inner boundary of G, i.e., the boundary of G with respect to the corresponding inner metric, where (Y, d) stands for a locally compact, non-complete and rectifiably connected metric space, and that G= f(G) is uniform in Y. The purpose of this paper is to prove that G is a John domain if f is M-quasihyperbolic in G and the restriction of f on the inner boundary of G is η-quasisymmetric with respect to the inner metric.

Original languageEnglish
JournalComputational Methods and Function Theory
DOIs
StateAccepted/In press - 2022

Keywords

  • Characterization
  • Gromov hyperbolicity
  • Inner uniformity
  • Quasisymmetry
  • Uniformity

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