English

The approximate conformal mapping of a disk onto domain with an acute angle

Complex Variables 2023-07-10 v1 Metric Geometry

Abstract

The method of boundary curve reparametrization is applied to construction of the approximate analytical conformal mapping of the unit disk onto an arbitrary given finite domain with a boundary smooth at every point but fininte number of acute angle points. The method is based on both the Fredholm equation solution and spline-interpolation. This approach consists of approximate solution of a linear system with unknown Fourier coefficients and construction of correction splines. The approximate mapping function has the form of a Cauchy integral. The method presentation is supported by demonstration of some examples. This method is applicable to the case of multiply connected domains with boundary angle points.

Keywords

Cite

@article{arxiv.2307.03516,
  title  = {The approximate conformal mapping of a disk onto domain with an acute angle},
  author = {Pyotr N. Ivanshin and Elena A. Shirokova},
  journal= {arXiv preprint arXiv:2307.03516},
  year   = {2023}
}

Comments

Accepted for publication in IJACM 11.01.23