Abstract
In this paper, we focus on exterior John domains. A John domain is called an exterior John domain if it is the exterior of a compact set. We prove that a quasiconformal mapping from the exterior of the closed unit ball to the exterior of a compact set is quasisymmetric with respect to the length inner distance if and only if its image is an exterior John domain. This result extends the classical results by Näkki and Väisälä in \({\mathbb R}^2\) (Expos Math 9:3–43, 1991, Thm. 7.4]) to arbitrary Euclidean space \({\mathbb R}^n\).
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Acknowledgements
The authors thank Prof. Yi Ru-Ya Zhang for many useful suggestions and comments. We also express gratitude to Prof. Jian-Feng Zhu for his interest in this work and for useful discussions during its preparation.
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Communicated by Pekka Koskela.
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Jinsong Liu was supported by National Key R &D Program of China (Grant no. 2021YFA1003100), NSFC (Grant no. 11925107), and Key Research Program of Frontier Sciences, CAS (Grant no. ZDBS-LY-7002)).
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Liu, J., Xuan, Y. Exterior John Domains and Quasisymmetric Mappings. Comput. Methods Funct. Theory 24, 7–25 (2024). https://doi.org/10.1007/s40315-023-00478-4
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DOI: https://doi.org/10.1007/s40315-023-00478-4