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 language | English |
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Journal | Forum Mathematicum |
DOIs | |
State | Published - 30 Sep 2022 |
Keywords
- Hölder domain
- Hölder continuity
- Gromov hyperbolic domain
- quasiconformal mapping
- quasihyperbolic metric
- uniformization