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    Schwarz-Christoffel mapping of multiply connected domains

    Date
    2004-12-01
    Author
    DeLillo, Thomas K.
    Elcrat, Alan R.
    Pfaltzgraff, J. A.
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    Citation
    Delillo, T., A. Elcrat, et al. (2004). "Schwarz-Christoffel mapping of multiply connected domains." Journal d'Analyse Mathématique 94(1): 17-47.
    Abstract
    A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivity m _> 2 thereby extending the results of Christoffel (1867) and Schwarz (1869) for m = 1 and Komatu (1945), m = 2. A formula for f, the conformal map of the exterior of m bounded disks to the exterior of m bounded disjoint polygons, is derived. The derivation characterizes the global preSchwarzian f" (z) If' (z) on the Riemann sphere in terms of its singularities on the sphere and its values on the m 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 the m boundary circles to the whole sphere.
    Description
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    URI
    http://hdl.handle.net/10057/6056
    http://dx.doi.org/10.1007/BF02789040
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