Circular Slits Map of Bounded Multiply Connected Regions

Spiral slits map and its inverse of bounded multiply connected regions

This paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse. The method is an extension of the author’s method for computing the Annulus with circular slits map of bounded multiply connected regions (see [Sangawi, A. W. K., Murid, A. H. M., Nasser, M. M. S.: Annulu...

Toeplitz Operators in Multiply Connected Regions

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...

Slit Map: Conformal Parameterization for Multiply Connected Surfaces

Surface parameterization is a fundamental tool in geometric modeling and processing. Most existing methods deal with simply connected disks. This work introduces a novel method to handle multiply connected surfaces based on holomorphic one-forms. The method maps genus zero surfaces with arbitrary number of boundaries to an annulus with concentric circular slits. Any two boundaries can be chosen...

Schwarz – Christoffel mappings to unbounded multiply connected polygonal regions

A formula for the generalized Schwarz–Christoffel conformal mapping from a bounded multiply connected circular domain to an unbounded multiply connected polygonal domain is derived. The formula for the derivative of the mapping function is shown to contain a product of powers of Schottky–Klein prime functions associated with the circular preimage domain. Two analytical checks of the new formula...