Asymptotics of the Conformal Modulus of Unbounded Symmetric Doubly Connected Domain Under Stretching

We describe the asymptotic behavior of the conformal modulus of an unbounded doubly connected planar domain, symmetric with respect to the coordinate axes, when stretched in the direction of the abscissa axis with coefficient tending to infinity. Therefore, we give a partial answer to a problem, sug...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-12, Vol.42 (12), p.2895-2904
Main Authors: Nasyrov, S. R., Nguyen Van Giang
Format: Article
Language:English
Subjects:
Algebra
Analysis
Asymptotic properties
Domains
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Quadrilaterals
Stretching
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Summary:We describe the asymptotic behavior of the conformal modulus of an unbounded doubly connected planar domain, symmetric with respect to the coordinate axes, when stretched in the direction of the abscissa axis with coefficient tending to infinity. Therefore, we give a partial answer to a problem, suggested by M. Vourinen, for the case of unbounded domains. We also use classical theorems by Ahlfors and Warshavskii to investigate the asymptotical behavior of the conformal modulus of a quadrilateral under stretching.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080221120258