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Статья
2017

Univalent conformal mappings onto polygonal domains with countable set of vertices by generalized Christoffel–Schwarz integral


E. N. KhasanovaE. N. Khasanova
Русская математика
https://doi.org/10.3103/S1066369X1707009X
Abstract / Full Text

We propose a formula for the conformalmapping of the upper half-plane onto a polygonal domain, which generalizes the Schwarz–Christoffel equation. It is obtained by terms of partial solution to the Hilbert boundary-value problem with a countable set of singularity points of the coefficients including a turbulence of logarithmic type at the infinity point. We also prove the existence of closed and univalent mappings.

Author information
  • Kazan State University of Architecture and Civil Engineering, ul. Zelyonaya 1, Kazan, 420043, RussiaE. N. Khasanova
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