On canonical conformal maps of multiply connected regions

Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions

and Applied Analysis 3 ΓM Γ2 Γ1

A General Theorem on Conformal Mapping of Multiply Connected Domains.

Numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions.

This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions. For each canonical region, two integral equations are solved before one can approximate the boundary values of the mapping function. Cauchy's-type integrals are used ...

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...

Toeplitz Operators in Multiply Connected Regions