Geodesic
Conformal mapping of circular multiply connected domains onto slit domains
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 286-297
The method of Riemann -- Hilbert problems is used to unify and to simplify construction of conformal mappings of multiply connected domains. Conformal mappings of arbitrary circular multiply connected domains onto the complex plane with slits of prescribed inclinations are constructed. The mappings are derived in terms of uniformly convergent Poincaré series. In the proposed method, no restriction on the location of the boundary circles is assumed. Convergence and implementation of the numerical method are discussed.
Classification : 30C30, 30E25
Keywords: Riemann, Hilbert problem, multiply connected domain, complex plane with slits 
@article{ETNA_2012__39__a10,
     author = {Czapla,  Roman and Mityushev,  Vladimir and Rylko,  Natalia},
     title = {Conformal mapping of circular multiply connected domains onto slit domains},
     journal = {Electronic transactions on numerical analysis},
     pages = {286--297},
     year = {2012},
     volume = {39},
     zbl = {1291.30043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a10/}
}
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AU  - Mityushev,  Vladimir
AU  - Rylko,  Natalia
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EP  - 297
VL  - 39
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%A Mityushev,  Vladimir
%A Rylko,  Natalia
%T Conformal mapping of circular multiply connected domains onto slit domains
%J Electronic transactions on numerical analysis
%D 2012
%P 286-297
%V 39
%U http://geodesic.mathdoc.fr/item/ETNA_2012__39__a10/
%G en
%F ETNA_2012__39__a10
Czapla,  Roman; Mityushev,  Vladimir; Rylko,  Natalia. Conformal mapping of circular multiply connected domains onto slit domains. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 286-297. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a10/