On conformal moduli of polygonal quadrilaterals
type: Item
instance of: scholarly article
title: On conformal moduli of polygonal quadrilaterals
zbMATH Open document ID: 1182.30011
author: V. N. Dubinin
author: M. Vuorinen
published in: Israel Journal of Mathematics
publication date: 2009-08-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0701387
review text: The authors study the change of conformal moduli of polygonal quadrilaterals under certain geometric transformations. Results of this type have applications in the theory of quasiconformal mappings, see [\textit{O. Lehto} and \textit{K. I. Virtanen}, Quasiconformal mappings in the plane. Translated from the German by K. W. Lucas. 2nd ed. Die Grundlehren der mathematischen Wissenschaften. Band 126. Berlin-Heidelberg-New York: Springer-Verlag (1973; Zbl 0267.30016)]. Examples of transformations considered in this paper are the motion of one vertex when others are kept fixed, rotation of sides, polarizations, symmetrizations, and averaging transformations. Some of the questions studied have been motivated by computational experiments, see [\textit{V. Heikkala, M. K. Vamanamurthy} and \textit{M. Vuorinen}, Comput. Methods Funct. Theory 9, No. 1, 75--109 (2009; Zbl 1198.33002)]. Inequalities concerning the behavior of the conformal modulus under these transformations are obtained. In addition, several examples and open problems are given.
reviewed by: A. Rasila
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 5600323
zbMATH Keywords: conformal modulus
zbMATH Keywords: generalized quadrilateral
zbMATH Keywords: geometric transformation
MaRDI profile type: Publication
OpenAlex ID: W2591713726
arXiv ID: math/0701387
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DOI: 10.1007/S11856-009-0043-8
description: scientific article