Journal d’Analyse Mathematique

, Volume 94, Issue 1, pp 17–47 | Cite as

Schwarz-Christoffel mapping of multiply connected domains

  • T. K. Delillo
  • A. R. Elcrat
  • J. A. Pfaltzgraff
Article

Abstract

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivitym≥2 thereby extending the results of Christoffel (1867) and Schwarz (1869) form=1 and Komatu (1945),m=2. A formula forf, the conformal map of the exterior ofm bounded disks to the exterior ofm bounded disjoint polygons, is derived. The derivation characterizes the global preSchwarzianf″ (z)/f′ (z) on the Riemann sphere in terms of its singularities on the sphere and its values on them boundary circles via the reflection principle and then identifies a singularity function with the same boundary behavior. The singularity function is constructed by a “method of images” infinite sequence of iterations of reflecting prevertex singularities from them boundary circles to the whole sphere.

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Copyright information

© The Hebrew University Magnes Press 2004

Authors and Affiliations

  • T. K. Delillo
    • 1
  • A. R. Elcrat
    • 1
  • J. A. Pfaltzgraff
    • 2
  1. 1.Department of Mathematics and StatisticsWichita State UniversityWichitaUSA
  2. 2.Department of Mathematics, CB 3250University of North CarolinaChapel HillUSA

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