数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1874-1882.doi: 10.1007/s10473-020-0616-5

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PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

林珍连1, 石擎天2   

  1. 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    2. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
  • 收稿日期:2019-05-20 修回日期:2020-07-31 出版日期:2020-12-25 发布日期:2020-12-30
  • 作者简介:Zhenlian LIN,E-mail:zhenlian@hqu.edu.cn;Qingtian SHI,E-mail:shiqingtian2013@gmail.com
  • 基金资助:
    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).

PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

Zhenlian LIN1, Qingtian SHI2   

  1. 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    2. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
  • Received:2019-05-20 Revised:2020-07-31 Online:2020-12-25 Published:2020-12-30
  • Supported by:
    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).

摘要: In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of $\Sigma_{K}^{0}$ have some gaps. Then we also find that the area derivative formula (1.6), which is used to estimate the area distortion of $\Sigma_{K}^{0}$, cannot be derived from [6], but that formula still holds for $\Sigma_{K}^{0}$ through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.

关键词: quasiconformal mapping, $\Sigma_{K}^{0}$, parametric representation, area distortion theorem, Cauchy transformation

Abstract: In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of $\Sigma_{K}^{0}$ have some gaps. Then we also find that the area derivative formula (1.6), which is used to estimate the area distortion of $\Sigma_{K}^{0}$, cannot be derived from [6], but that formula still holds for $\Sigma_{K}^{0}$ through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.

Key words: quasiconformal mapping, $\Sigma_{K}^{0}$, parametric representation, area distortion theorem, Cauchy transformation

中图分类号: 

  • 30C62