Gromov hyperbolicity and unbounded uniform domains

Qingshan Zhou, Yuehui He*, Antti Rasila, Tiantian Guan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper focuses on Gromov hyperbolic characterizations of unbounded uniform domains. Let G⊊Rn be an unbounded domain. We prove that the following conditions are quantitatively equivalent: (1) G is uniform; (2) G is Gromov hyperbolic with respect to the quasihyperbolic metric and linearly locally connected; (3) G is Gromov hyperbolic with respect to the quasihyperbolic metric and there exists a naturally quasisymmetric correspondence between its Euclidean boundary and the punctured Gromov boundary equipped with a Hamenstädt metric (defined by using a Busemann function). As an application, we investigate the boundary quasisymmetric extensions of quasiconformal mappings, and of more generally rough quasi-isometries between unbounded domains with respect to the quasihyperbolic metrics.

Original languageEnglish
JournalManuscripta Mathematica
DOIs
StateAccepted/In press - 2024

Keywords

  • 30F45
  • Primary 30C65 Secondary 30C20

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