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Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains

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Abstract

We have recently derived a Schwarz-Christoffel formula for the conformal mapping of the exterior of a finite number of disks to the exterior of a set of polygonal curves [5]. In this work we show how to formulate a set of equations for determining the parameters of such a map. A number of examples are computed, including exteriors of multiple slits. We also recall the derivation of the mapping formulae and give a new formula for the doubly connected case.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wichita State University, Wichita, KS, 67260-0033, USA

    Thomas K. DeLillo & Tobin A. Driscoll

  2. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Alan R. Elcrat

  3. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    John A. Pfaltzgraff

Authors
  1. Thomas K. DeLillo
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  2. Tobin A. Driscoll
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  3. Alan R. Elcrat
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  4. John A. Pfaltzgraff
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Correspondence to Thomas K. DeLillo.

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DeLillo, T.K., Driscoll, T.A., Elcrat, A.R. et al. Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains. Comput. Methods Funct. Theory 6, 301–315 (2006). https://doi.org/10.1007/BF03321616

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  • DOI: https://doi.org/10.1007/BF03321616

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