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Conformal mappings onto prescribed regions via optimization techniques

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Summary

All well known extremal principles for conformal mappings of simply connected regionsR yield mappings onto disksD. It is shown here that given an arbitrary star shaped regionD as range a corresponding extremal principle is valid just by replacing the ordinary modulus inℂ by a suitable positively homogeneous functional. If the star shaped regionD (bounded or not) is a convex polygon the extremal principle is equivalent to a linear (but infinite) programming problem, which can be solved approximately by passing to an ordinary (i.e. finite) linear programming problem. A numerical example whereR is a disk and the rangeD is an infinite strip is given.

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  1. Institut für Angewandte Mathematik, Universität Hamburg, Bundesstraße 55, 2000, Hamburg 13, Germany (Fed. Rep.)

    Gerhard Opfer

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  1. Gerhard Opfer
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Opfer, G. Conformal mappings onto prescribed regions via optimization techniques. Numer. Math. 35, 189–200 (1980). https://doi.org/10.1007/BF01396315

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