Geodesic
Solution of the parameter problem of the Schwarz–Christoffel conformal mapping of the interior (exterior) of a circle onto the interior (exterior) of a polygon
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 82 (2023), pp. 28-38

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We propose an analytical solution of the parameter problem of the Schwarz–Christoffel conformal mapping of the interior (exterior) of a circle onto the interior (exterior) of a polygon by use of the behavior of the Newtonian simple layer and logarithmic potentials equal to a constant inside of a simply connected domain.
Keywords: conformal mapping, Schwarz–Christoffel parameter problem, potential method. 
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     author = {N. A. Trubaev},
     title = {Solution of the parameter problem of the {Schwarz{\textendash}Christoffel} conformal mapping of the interior (exterior) of a circle onto the interior (exterior) of a polygon},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {28--38},
     publisher = {mathdoc},
     number = {82},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_82_a2/}
}
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N. A. Trubaev. Solution of the parameter problem of the Schwarz–Christoffel conformal mapping of the interior (exterior) of a circle onto the interior (exterior) of a polygon. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 82 (2023), pp. 28-38. http://geodesic.mathdoc.fr/item/VTGU_2023_82_a2/