Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics

Qingshan Zhou, Yaxiang Li*, Antti Rasila

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a double cone arc. This result provides a new approach to an elementary metric geometry question, formulated by Heinonen (Quasiconformal mappings onto John domains. Rev Math Iberoam 5:97–123, 1989), which has been studied by Gehring et al. (Quasihyperbolic geodesics in John domains. Math Scand 36:75–92, 1989). As an application, we obtain a simple geometric condition connecting uniformity of a metric space with the existence of a Gromov hyperbolic quasihyperbolization.

Original languageEnglish
Article number228
JournalJournal of Geometric Analysis
Issue number9
StatePublished - Sep 2022


  • Gromov hyperbolic spaces
  • John spaces
  • Quasihyperbolic geodesic
  • Quasihyperbolic metric


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