Parametric Representations of Quasiconformal Mappings

In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of Σ 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 Σ K 0 , cannot be derived from [6], but that...

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Bibliographic Details
Published in:Acta mathematica scientia 2020-11, Vol.40 (6), p.1874-1882
Main Authors: Lin, Zhenlian, Shi, Qingtian
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:In this article, we first give two simple examples to illustrate that two types of parametric representation of the family of Σ 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 Σ K 0 , cannot be derived from [6], but that formula still holds for Σ K 0 through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-020-0616-5