Conformal mapping of multiply connected domains. II.

A General Theorem on Conformal Mapping of Multiply Connected Domains.

Green's Functions for Multiply Connected Domains via Conformal Mapping

A method is described for the computation of the Green’s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz–Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K −...

Schwarz-christoffel Mapping of Multiply Connected Domains

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivity m ≥ 2 thereby extending the results of Christoffel (1867) and Schwarz (1869) for m = 1 and Komatu (1945), m = 2. A formula for f, the conformal map of the exterior of m bounded disks to the exterior of m bounded, disjoint polygons, is derived. The derivation characterizes the global preSchwarzian f...

Conformal Mapping of Multiply Connected Riemann Domains by a Variational Approach

We show with a new variational approach that any Riemannian metric on a multiply connected schlicht domain in R can be represented by globally conformal parameters. This yields a “Riemannian version” of Koebe’s mapping theorem. Mathematics Subject Classification (2000): 30C20, 49J45, 49Q05, 49Q10, 53A10

Numerical conformal mapping of multiply connected domains to regions with circular boundaries

We propose a method to map a multiply connected bounded planar region conformally to a bounded region with circular boundaries. The norm of the derivative of such a conformal map satisfies the Laplace equationwith a nonlinear Neumann type boundary condition.We analyze the singular behavior at corners of the boundary and separate the major singular part. The remaining smooth part solves a variat...