Geodesic
Univalent conformal mappings by generalized Christoffel--Schwartz integral onto polygonal domains with countable set of vertices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 74-83.

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We obtain a formula for the conformal mapping of the upper half-plane onto a polygonal domain. This structural formula generalizes the Schwartz–Christoffel equation and is written with the use of partial solution to the Hilbert boundary-value problem with a countable set of points of discontinuity of the coefficients and with turbulence at infinity of logarithmic type. We also prove closedness and existence of univalent mappings among given ones.
Keywords: Schwartz–Christoffel equation, conformal mapping, Hilbert boundary-value problem
Mots-clés : univalence. 
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E. N. Khasanova. Univalent conformal mappings by generalized Christoffel--Schwartz integral onto polygonal domains with countable set of vertices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 74-83. http://geodesic.mathdoc.fr/item/IVM_2017_7_a8/

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