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数学与物理学

Riemann 映照的一种迭代构造

  • 邓富声 ,
  • 姜炜文 ,
  • 张旭俊
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  • 中国科学院大学数学科学学院, 北京 100049

收稿日期: 2019-07-16

  修回日期: 2019-09-30

  网络出版日期: 2021-03-05

基金资助

Supported by National Nature Science Foundation of China (11871451) and University of Chinese Academy of Sciences (Y8540XX112)

An iterative construction of Riemann mappings

  • DENG Fusheng ,
  • JIANG Weiwen ,
  • ZHANG Xujun
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2019-07-16

  Revised date: 2019-09-30

  Online published: 2021-03-05

Supported by

Supported by National Nature Science Foundation of China (11871451) and University of Chinese Academy of Sciences (Y8540XX112)

摘要

给出Riemann映照递归逼近的一个显示构造,该方式是受Koebe证明Riemann映照定理的思想的启发。

本文引用格式

邓富声 , 姜炜文 , 张旭俊 . Riemann 映照的一种迭代构造[J]. 中国科学院大学学报, 2021 , 38(1) : 29 -31 . DOI: 10.7523/j.issn.2095-6134.2021.01.004

Abstract

In this note, we give an explicit construction of iterative approximation of Riemann mappings. Our method is motivated by Koebe’s proof of the Riemann mapping theorem.

参考文献

[1] Ahlfors L. Complex analysis. An introduction to the theory of analytic functions of one com-plex variable[M]. 3rd ed. International Series International Series in Pure and Applied Mathematics. New York:McGraw-Hill Book Co, 1978.
[2] Thurston W. Three-dimensional geometry and topology. Vol. 1[M]. Levy S. Princeton Mathematical Series, 35. Princeton:Princeton University Press, NJ, 1997.
[3] He Z X, Schramm O. The C-convergence of hexagonal disk packings to the Riemann map[J]. Acta Math, 1998, 180:219-245.
[4] Bishop E. Foundations of constructive analysis[M]. New York:McGraw-Hill, 1967.
[5] Cheng H. A constructive Riemann Mapping theorem[J]. Pacific J Math,1973, 144:435-454.
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