Numerical computation of the Ahlfors map of a multiply connected planar domain
type: Item
instance of: scholarly article
title: Numerical computation of the Ahlfors map of a multiply connected planar domain
zbMATH Open document ID: 0598.30010
DOI: 10.1016/0022-247X(86)90211-8
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: If D is an n-connected, bounded, planar domain with \(C^ 2\)-boundary components with \(a\in D\), then the Ahlfors map \(f_ a\) for D at a is a branched n to one covering map of D onto the unit disc \(\Delta\), \(f_ a(a)=0\), \(f_ a\) and \(f_ a'\) extend continuously to \(\bar D;\) each boundary curve of D is mapped one-to-one onto the boundary of \(\Delta\). Following an idea of \textit{N. Kerzman} and \textit{E. M. Stein} in the simply connected case [Math. Ann. 236, 85-93 (1978; Zbl 0419.30012)] the author derives a representation of \(f_ a\) as a quotient of two functions which satisfy linear Fredholm integral equations of the second kind with skew Hermitian kernels. This leads to a numerical method for computing \(f_ a\); numerical computations are not reported.
Mathematics Subject Classification ID: 30C30
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 65E05
zbMATH DE Number: 3964301
zbMATH Keywords: Ahlfors map
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: skew Hermitian kernels
author: Steven R. Bell
MaRDI profile type: Publication
cites work: Q4750106
cites work: Q5610508
cites work: Q4750081
cites work: Schwarz's Lemma and the Szego Kernel Function
cites work: Iterative solution of transonic flows over airfoils and wings, including flows at mach 1
cites work: The Cauchy kernel, the Szegö kernel, and the Riemann mapping function
cites work: Numerical conformal mapping via the Szegö kernel
cites work: On Bounded Analytic Functions
cites work: Q5815016
full work available at URL: 0022-247x(86)90211-8
OpenAlex ID: W2072219776
description: scientific article; zbMATH DE number 3964301