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On Kufarev’s method of determining the parameters in the Schwarz- Christoffel integral. (English. Russian original) Zbl 0829.30005
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 445-448 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 1, 14-16 (1994).
Let $$D_n$$ be a polygonal domain, and let $$D_n (t)$$ be obtained from $$D_n$$ by introducing a rectilinear slit of length $$\Lambda_n (t)$$. Let $$a_j(t)$$, $$c(t)$$ be the accessory parameters in the Schwarz- Christoffel map from the upper half plane $$H$$ onto $$D_n (t)$$. The authors show that these satisfy a nonlinear system of ordinary differential equations, with given initial values if the mapping from $$H$$ to $$D_n$$ is known. This system has a unique solution for small values of $$t$$. In view of the work of Trefethen, this method will hardly be suited for effective polygonal mappings.
Reviewer: D.Gaier (Gießen)
##### MSC:
 30C30 Schwarz-Christoffel-type mappings
##### Keywords:
Löwner differential equation