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Geometric characterizations of Gromov hyperbolic Hölder domains

  • Qingshan Zhou and Antti Rasila ORCID logo EMAIL logo
Published/Copyright: September 30, 2022

Abstract

In this paper, we investigate Hölder continuity of quasiconformal mappings in n 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.

MSC 2010: 30C65; 30C20; 30F45

Communicated by Karin Melnick


Award Identifier / Grant number: 11901090

Award Identifier / Grant number: 12071121

Award Identifier / Grant number: 11971124

Award Identifier / Grant number: 2021KTSCX116

Award Identifier / Grant number: 2022A1515012441

Award Identifier / Grant number: 2021A1515012289

Award Identifier / Grant number: 2021A1515110484

Award Identifier / Grant number: 2021A1515010326

Funding statement: Qingshan Zhou was partly supported by NNSF of China (Nos. 11901090, 12071121), by Department of Education of Guangdong Province, China (No. 2021KTSCX116), and by Guangdong Basic and Applied Basic Research Foundation (Nos. 2022A1515012441, 2021A1515012289, 2021A1515110484). Antti Rasila was supported by NNSF of China (No. 11971124), and NSF of Guangdong Province (No. 2021A1515010326).

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Received: 2022-03-25
Revised: 2022-08-08
Published Online: 2022-09-30
Published in Print: 2022-11-01

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