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

Authors
  • Nasyrov, S. R.1
  • Nguyen Van Giang,1
  • 1 Kazan Federal University, Kazan, Tatarstan, 420008, Russia , Kazan (Russia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Dec 13, 2021
Volume
42
Issue
12
Pages
2895–2904
Identifiers
DOI: 10.1134/S1995080221120258
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

AbstractWe 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.

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