Geodesic
Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc
Annales Polonici Mathematici, Tome 68 (1998) no. 3, pp. 227-236.

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The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
DOI : 10.4064/ap-68-3-227-236
Keywords: conformal mapping, boundary value problem, functional equation

Vladimir Mityushev 1

1 
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Vladimir Mityushev. Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc. Annales Polonici Mathematici, Tome 68 (1998) no. 3, pp. 227-236. doi : 10.4064/ap-68-3-227-236. http://geodesic.mathdoc.fr/articles/10.4064/ap-68-3-227-236/

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