PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

doi:10.1007/s10473-020-0616-5

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

PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

林珍连¹, 石擎天²

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. 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/Abstract

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

林珍连, 石擎天. PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS[J]. 数学物理学报(英文版), 2020, 40(6): 1874-1882.

Zhenlian LIN, Qingtian SHI. PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS[J]. Acta mathematica scientia,Series B, 2020, 40(6): 1874-1882.

参考文献

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[12] Qi Y, Shi Q -T. Estimations of convexity radius and the norm of pre-Schwarz derivative for close to convex harmonic mappings. Acta Math Sci, 2016, 36A(6):1057-1066
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PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS

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