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. 
@article{IVM_2017_7_a8,
     author = {E. N. Khasanova},
     title = {Univalent conformal mappings by generalized {Christoffel--Schwartz} integral onto polygonal domains with countable set of vertices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--83},
     publisher = {mathdoc},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_7_a8/}
}
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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/