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Topological Angles and Freely Quasiconformal Mappings in Real Banach Spaces

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In this paper, several characterizations for both quasisymmetric mappings and freely quasiconformal mappings in real Banach spaces are established. Also, we get a characterization for a freely quasiconformal mapping to be quasisymmetric. All these characterizations consist of inequalities in terms of the point measure and the inner measure of topological angles, which were introduced by Agard and Gehring (Proc Lond Math Soc 3(14a):1–21, 1965). Also, we construct two examples which show that certain conditions in the obtained characterizations can not be removed.

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Acknowledgements

The authors thank an anonymous reader for the careful reading of this paper and very useful comments on this paper. Zhiqiang Yang was partly supported by NNSF of China under the number 12071121. Qingshan Zhou was partly supported by NNSF of China (No. 11901090), by Department of Education of Guangdong Province, China (No. 2021KTSCX116), by Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515012289), and Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (No. 2020B1212030010).

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Authors and Affiliations

  1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Zhiqiang Yang

  2. School of Mathematics and Big Data, Foshan University, Foshan, 528000, Guangdong, People’s Republic of China

    Qingshan Zhou

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  1. Zhiqiang Yang
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  2. Qingshan Zhou
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Communicated by Vladimir V. Andrievskii.

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Yang, Z., Zhou, Q. Topological Angles and Freely Quasiconformal Mappings in Real Banach Spaces. Comput. Methods Funct. Theory 23, 347–368 (2023). https://doi.org/10.1007/s40315-022-00445-5

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