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- Title
Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics.
- Authors
Zhou, Qingshan; Li, Yaxiang; Rasila, Antti
- Abstract
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.
- Publication
Journal of Geometric Analysis, 2022, Vol 32, Issue 9, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-022-00968-2