Gromov hyperbolicity and unbounded uniform domains
- Resource Type
- Original Paper
- Authors
- Zhou, Qingshan; He, Yuehui; Rasila, Antti; Guan, Tiantian
- Source
- manuscripta mathematica. 174(3-4):1075-1101
- Subject
- Primary 30C65 Secondary 30C20
30F45
- Language
- English
- ISSN
- 0025-2611
1432-1785
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.