Geometric characterizations of Gromov hyperbolic Hölder domains

Qingshan Zhou, Antti Rasila*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate Hölder continuity of quasiconformal mappings in Rn from the points of view of quasihyperbolic geometry and the theory of Gromov hyperbolic spaces. We establish several characterizations of Gromov hyperbolic domains satisfying the Gehring–Martio-type quasihyperbolic boundary conditions. As applications, we generalize certain results concerning Hölder continuity of conformal mappings, establishing counterparts of results of Becker and Pommerenke, Smith and Stegenga, and Näkki and Palka in higher-dimensional Euclidean spaces.
Original languageEnglish
JournalForum Mathematicum
DOIs
StatePublished - 30 Sep 2022

Keywords

  • Hölder domain
  • Hölder continuity
  • Gromov hyperbolic domain
  • quasiconformal mapping
  • quasihyperbolic metric
  • uniformization

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