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Koebe Type Theorems and Pre-Schwarzian of Harmonic K-quasiconformal Mappings, and Their Applications

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Abstract

In this article, we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings. Then we use it to obtain an asymptotically Koebe type distortion theorem, a coefficients estimate, a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings. At last, we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421002, P. R. China

    Shao Lin Chen

  2. Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, 421002, P. R. China

    Shao Lin Chen

  3. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    Saminathan Ponnusamy

Authors
  1. Shao Lin Chen
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  2. Saminathan Ponnusamy
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Correspondence to Shao Lin Chen.

Additional information

The first author was partly supported by National Natural Science Foundation of China (Grant No. 12071116), the Key Projects of Hunan Provincial Department of Education (Grant No. 21A0429), the Discipline Special Research Projects of Hengyang Normal University (Grant No. XKZX21002), the Science and Technology Plan Project of Hunan Province (Grant No. 2016TP1020), and the Application-Oriented Characterized Disciplines, Double First-Class University Project of Hunan Province (Xiangjiaotong [2018]469). The work of the second author was supported by Mathematical Research Impact Centric Support (MATRICS) of the Department of Science and Technology (DST), India (MTR/2017/000367).

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Chen, S.L., Ponnusamy, S. Koebe Type Theorems and Pre-Schwarzian of Harmonic K-quasiconformal Mappings, and Their Applications. Acta. Math. Sin.-English Ser. 38, 1965–1980 (2022). https://doi.org/10.1007/s10114-022-1012-y

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  • DOI: https://doi.org/10.1007/s10114-022-1012-y

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