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

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Abstract

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.

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Funding

The work of the first author is supported by the development program of the Volga Region Mathematical Center (agreement no. 075-02-2021-1393).

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Authors and Affiliations

  1. Kazan Federal University, 420008, Kazan, Tatarstan, Russia

    S. R. Nasyrov &  Nguyen Van Giang

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  1. S. R. Nasyrov
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  2. Nguyen Van Giang
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Correspondence to S. R. Nasyrov or Nguyen Van Giang.

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(Submitted by F. G. Avhadiev)

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Nasyrov, S.R., Nguyen Van Giang Asymptotics of the Conformal Modulus of Unbounded Symmetric Doubly Connected Domain Under Stretching. Lobachevskii J Math 42, 2895–2904 (2021). https://doi.org/10.1134/S1995080221120258

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  • DOI: https://doi.org/10.1134/S1995080221120258

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