On the search for parameters of a conformal mapping from a half-plane to a circular polygon

The problem of constructing a conformal mapping from a half-plane to a circular polygon is considered. The preimages of the vertices of the polygon and accessory parameters are determined by the generalized method of P. P. Kufarev for determining the parameters in the Christoffel–Schwarz integral. The method is based on the Loewner equation with boundary normalization. The problem of constructing a mapping from a half-plane onto the exterior of a polygon with a boundary consisting of straight-line segments is solved separately. Examples of mappings whose parameters are found by the Kufarev method are given.