Numerical computation of the Ahlfors map of a multiply connected planar domain
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.
scientific article; zbMATH DE number 3964301