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Parametric Representations of Quasiconformal Mappings

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Abstract

In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of Σ0K have some gaps. Then we also find that the area derivative formula (1.6), which is used to estimate the area distortion of Σ0K , cannot be derived from [6], but that formula still holds for Σ0K through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Zhenlian Lin

  2. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, 362000, China

    Qingtian Shi

Authors
  1. Zhenlian Lin
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  2. Qingtian Shi
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Correspondence to Zhenlian Lin or Qingtian Shi.

Additional information

This work is supported by National Natural Science Foundation of China (11971182), the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-PY402), Research projects of Young and Middle-aged Teacher’s Education of Fujian Province (JAT190508) and Scientific research project of Quanzhou Normal University (H19009).

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Lin, Z., Shi, Q. Parametric Representations of Quasiconformal Mappings. Acta Math Sci 40, 1874–1882 (2020). https://doi.org/10.1007/s10473-020-0616-5

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  • DOI: https://doi.org/10.1007/s10473-020-0616-5

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