SLIT MAPS AND SCHWARZ-CHRISTOFFEL MAPS FOR MULTIPLY CONNECTED DOMAINS

We review recent derivations of formulas for conformal maps from finitely connected domains with circular holes to canonical radial or circular slit domains . The formulas are infinite products based on simple reflection arguments. An earlier similar derivation of the Schwar z-Christoffel formula for the bounded multiply connected case and recent progress in its numerical implementation ar e also reviewed. We give some sample calculations with a reflection method and an estimate of its accuracy. We also di scuss the relation of our approach to that of D. Crowdy and J. Marshall. In addition, a slit map calculation using La urent series computed by the least squares method in place of the reflection method is given as an example of a possi ble direction for future improvements in the numerics.

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