Abstract
In this paper, we prove that a proper subdomain \(\Omega \) of \(\mathbb {R}^n\) equipped with the metric \(i_{\Omega }\), recently introduced by Nikolov and Andreev, is Gromov hyperbolic. We also show that there is a natural quasisymmetric correspondence between the Euclidean boundary of \(\Omega \) (with respect to \(\overline{\mathbb {R}^n}\)) and the Gromov boundary of \((\Omega ,i_\Omega )\).
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The authors are grateful for the constructive remarks of the referee.
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Qianghua Luo was supported by Guangdong Basic and Applied Basic Research Foundation (No. 2023A1515110902). Antti Rasila was supported by NNSF of China (No. 11971124) by NSF of Guangdong Province (No. 2021A1515010326 and 2024A1515010467), and by Li Ka Shing Foundation (No. 2024LKSFG06). Ye Wang was supported by Huzhou Natural Science Foundation (No. 2022YZ37). Qingshan Zhou was partly supported by NNSF of China (No. 12201115), by Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515012441), and by Department of Education of Guangdong Province, China (No. 2021KTSCX116).
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Luo, Q., Rasila, A., Wang, Y. et al. The Nikolov–Andreev Metric and Gromov Hyperbolicity. Mediterr. J. Math. 21, 105 (2024). https://doi.org/10.1007/s00009-024-02655-8
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DOI: https://doi.org/10.1007/s00009-024-02655-8