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Mat. Zametki, 2018, Volume 103, Issue 4, Pages 503–518 (Mi mz11525)  

Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching

D. N. Dautova, S. R. Nasyrov

Kazan (Volga Region) Federal University

Abstract: An asymptotic formula for the conformal module of a doubly connected domain symmetric about the abscissa axis under an unbounded stretching in the direction of this axis is obtained. Thereby, in the case of symmetric domains, a question asked by Vuorinen is answered.

Keywords: conformal module, doubly connected domain, quadrilateral, quasiconformal mapping, convergence of domains to a kernel, prime ends of a plane domain.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00282
This work was supported by the Russian Foundation for Basic Research under grant 17-01-00282.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11525

Full text: PDF file (606 kB)
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English version:
Mathematical Notes, 2018, 103:4, 537–549

Bibliographic databases:

UDC: 517.5
Received: 14.01.2017
Revised: 10.04.2017

Citation: D. N. Dautova, S. R. Nasyrov, “Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching”, Mat. Zametki, 103:4 (2018), 503–518; Math. Notes, 103:4 (2018), 537–549

Citation in format AMSBIB
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