Geodesic
Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 503-518.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : conformal module, convergence of domains to a kernel
Keywords: doubly connected domain, quadrilateral, quasiconformal mapping, prime ends of a plane domain. 
@article{MZM_2018_103_4_a2,
     author = {D. N. Dautova and S. R. Nasyrov},
     title = {Asymptotics of the {Modules} of {Mirror} {Symmetric} {Doubly} {Connected} {Domains} under {Stretching}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {503--518},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a2/}
}
TY  - JOUR
AU  - D. N. Dautova
AU  - S. R. Nasyrov
TI  - Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching
JO  - Matematičeskie zametki
PY  - 2018
SP  - 503
EP  - 518
VL  - 103
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a2/
LA  - ru
ID  - MZM_2018_103_4_a2
ER  - 
%0 Journal Article
%A D. N. Dautova
%A S. R. Nasyrov
%T Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching
%J Matematičeskie zametki
%D 2018
%P 503-518
%V 103
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a2/
%G ru
%F MZM_2018_103_4_a2
D. N. Dautova; S. R. Nasyrov. Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 503-518. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a2/

[1] R. Kühnau, “The conformal module of quadrilaterals and of rings”, Handbook of Complex Analysis: Geometric Function Theory, Vol. 2, Elsevier, Amsterdam, 2005, 99–129 | MR | Zbl

[2] L. Alfors, Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969 | MR | Zbl

[3] D. Betsakos, K. Samuelsson, M. Vuorinen, “The computation of capacity of planar condensers”, Publ. Inst. Math. (Beograd) (N.S.), 75 (89) (2004), 233–252 | DOI | MR | Zbl

[4] V. N. Dubinin, M. Vuorinen, “On conformal moduli of polygonal quadrilaterals”, Israel J. Math., 171:1 (2009), 111–125 | DOI | MR | Zbl

[5] H. Hakula, A. Rasila, M. Vuorinen, “On moduli of rings and quadrilaterals: algorithms and experiments”, SIAM J. Sci. Comput., 33:1 (2011), 279–302 | DOI | MR | Zbl

[6] H. Hakula, A. Rasila, M. Vuorinen, Conformal Modulus on Domains With Strong Singularities and Cusps, 2015, arXiv: 1501.06765

[7] S. R. Nasyrov, “Conformal mappings of stretched polyominoes onto half-plane”, Lobachevskii J. Math., 38:3 (2017), 494–501 | MR | Zbl

[8] S. R. Nasyrov, “Riemann–Schwarz reflection principle and asymptotics of modules of rectangular frames”, Comput. Methods Funct. Theory, 15:1 (2015), 59–74 | DOI | MR | Zbl

[9] N. Papamichael, N. Stylianopoulos, Numerical Conformal Mapping. Domain Decomposition and the Mapping of Quadrilaterals, World Sci. Publ., Hackensack, NJ, 2010 | MR | Zbl

[10] M. Vuorinen, X. Zhang, “On exterior moduli of quadrilaterals and special functions”, J. Fixed Point Theory Appl., 13:1 (2013), 215–230 | DOI | MR | Zbl

[11] D. N. Dautova, “Asimptotika modulei rombovidnykh okon”, Materialy Dvenadtsatoi molodezhnoi nauchnoi shkoly-konferentsii “Lobachevskie chteniya – 2013”, Tr. Matem. tsentra im. N. I. Lobachevskogo, 47, Izd-vo Kazansk. matem. ob-va, Kazan, 2013, 39–40

[12] L. Ahlfors, Conformal Invariants. Topics in Geometric Function Theory, AMS Chelsea Publ., Providence, RI, 1973 | MR | Zbl

[13] M. A. Evgrafov, Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR | Zbl

[14] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[15] S. R. Nasyrov, Geometricheskie problemy teorii razvetvlennykh nakrytii rimanovykh poverkhnostei, Magarif, Kazan, 2008

[16] G. D. Suvorov, Prostye kontsy i posledovatelnosti ploskikh otobrazhenii, Naukova dumka, Kiev, 1986 | MR

[17] A. Vasil'ev, Moduli of Families of Curves for Conformal and Quasiconformal Mappings, Lecture Notes in Math., 1788, Springer-Verlag, Berlin, 2002 | DOI | MR | Zbl

[18] M. A. Evgrafov, Analiticheskie funktsii, Fizmatlit, M., 1991 | MR | Zbl

[19] V. M. Miklyukov, Konformnoe otobrazhenie neregulyarnoi poverkhnosti i ego primenenie, Izd-vo Volgogradsk. gos. un-ta, Volgograd, 2005

[20] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR | Zbl