Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Schwarz-Christoffel Mapping of Bounded, Multiply Connected Domains

Schwarz-Christoffel Mapping of Bounded, Multiply Connected Domains A Schwarz-Christoffel formula for conformal maps from the exterior of a finite number of disks to the exterior of polygonal curves was derived by DeLillo, Elcrat, and Pfaltzgraff in [9] using the Reflection Principle. The derivative of the map is expressed as an infinite product. In this paper, the formula for the map from bounded circular domains to bounded polygonal domains is derived by the same method. Convergence of the resulting infinite product is proved for sufficiently well-separated domains. A formula for the bounded case was also derived by Crowdy in [5] using Schottky-Klein prime functions. We show that Crowdy’s formula can be reduced to ours. In addition, we discuss the relation of these formulae to the Poincaré theta series for functions automorphic under the Schottky group of Moebius transformations generated by reflections in circles. We also derive a formula for the map to circular slit domains. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Schwarz-Christoffel Mapping of Bounded, Multiply Connected Domains

Loading next page...
 
/lp/springer-journals/schwarz-christoffel-mapping-of-bounded-multiply-connected-domains-C4wk4DWoo0

References (21)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321615
Publisher site
See Article on Publisher Site

Abstract

A Schwarz-Christoffel formula for conformal maps from the exterior of a finite number of disks to the exterior of polygonal curves was derived by DeLillo, Elcrat, and Pfaltzgraff in [9] using the Reflection Principle. The derivative of the map is expressed as an infinite product. In this paper, the formula for the map from bounded circular domains to bounded polygonal domains is derived by the same method. Convergence of the resulting infinite product is proved for sufficiently well-separated domains. A formula for the bounded case was also derived by Crowdy in [5] using Schottky-Klein prime functions. We show that Crowdy’s formula can be reduced to ours. In addition, we discuss the relation of these formulae to the Poincaré theta series for functions automorphic under the Schottky group of Moebius transformations generated by reflections in circles. We also derive a formula for the map to circular slit domains.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

There are no references for this article.