Asymptotics of the Exterior Conformal Modulus of a Quadrilateral under Stretching Map

In this paper, we focus on studying the distortion of the exterior conformal modulus of a quadriilateral of a sufficiently arbitrary form under the stretching map along the abscissa axis with coefficient . By using the properties of quasiconformal transformations and taking into account some facts f...

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Bibliographic Details
Published in:Russian mathematics 2023-05, Vol.67 (5), p.66-71
Main Authors: Nasyrov, S. R., Nguyen, G. V.
Format: Article
Language:English
Subjects:
Asymptotic properties
Elliptic functions
Mathematics
Mathematics and Statistics
Quadrilaterals
Stretching
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Summary:In this paper, we focus on studying the distortion of the exterior conformal modulus of a quadriilateral of a sufficiently arbitrary form under the stretching map along the abscissa axis with coefficient . By using the properties of quasiconformal transformations and taking into account some facts from the theory of elliptic integrals, we confirm that the asymptotic behavior of this modulus does not depend on the shape of the boundary of the quadrilateral. Especially, it is equivalent to as . Therefore, we give a solution to the Vuorinen problem for the exterior conformal modulus of a sufficiently arbitrary quadrilateral.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X23050080