Geometric characterizations of Gromov hyperbolic Hölder domains

Qingshan Zhou; Antti Rasila

doi:10.1515/forum-2022-0095

Geometric characterizations of Gromov hyperbolic Hölder domains

Qingshan Zhou, Antti Rasila^*

^*Corresponding author for this work

Mathematics with Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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
Journal	Forum Mathematicum
DOIs	https://doi.org/10.1515/forum-2022-0095
State	Published - 30 Sep 2022

Keywords

Hölder domain
Hölder continuity
Gromov hyperbolic domain
quasiconformal mapping
quasihyperbolic metric
uniformization

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abstract = "In this paper, we investigate H{\"o}lder 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 H{\"o}lder continuity of conformal mappings, establishing counterparts of results of Becker and Pommerenke, Smith and Stegenga, and N{\"a}kki and Palka in higher-dimensional Euclidean spaces.",

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AU - Rasila, Antti

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N2 - 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.

AB - 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.

KW - Hölder domain

KW - Hölder continuity

KW - Gromov hyperbolic domain

KW - quasiconformal mapping

KW - quasihyperbolic metric

KW - uniformization

U2 - 10.1515/forum-2022-0095

DO - 10.1515/forum-2022-0095

M3 - 文章

SN - 0933-7741

JO - Forum Mathematicum

JF - Forum Mathematicum

ER -

Geometric characterizations of Gromov hyperbolic Hölder domains

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Keywords

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