Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1874-1882.doi: 10.1007/s10473-020-0616-5

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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).

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

CLC Number: 

  • 30C62