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Landau–Bloch Type Theorems for Certain Subclasses for Polyharmonic Mappings

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Abstract

In this paper, we first establish a Landau–Bloch type theorem for certain bounded polyharmonic mappings, which improves upon a result given by Bai et al. (Complex Anal Oper Theory, 13(2):321–340, 2019). Then, we establish three new versions of Landau–Bloch type theorems for polyharmonic mappings, and obtain several sharp results. Finally, we provide four bi-Lipschitz theorems for these subclasses of polyharmonic mappings.

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The authors declare that this research is purely theoretical and does not associate with any data.

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Acknowledgements

This research was partly supported by Guangdong Natural Science Foundations (Grant No. 2021A1515010058). The work of the first author was also supported by National Natural Science Foundation, China (Grant No. 61976104). The authors of this paper thank the referees very much for their valuable comments and suggestions for this paper.

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Authors and Affiliations

  1. School of Mathematics, Jiaying University, Meizhou, 514015, Guangdong, People’s Republic of China

    Xi Luo

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Xi Luo & Ming-Sheng Liu

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  1. Xi Luo
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  2. Ming-Sheng Liu
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Correspondence to Ming-Sheng Liu.

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Luo, X., Liu, MS. Landau–Bloch Type Theorems for Certain Subclasses for Polyharmonic Mappings. Comput. Methods Funct. Theory 23, 303–325 (2023). https://doi.org/10.1007/s40315-022-00441-9

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  • DOI: https://doi.org/10.1007/s40315-022-00441-9

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