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Variation of diametrically symmetric or elliptically schlicht conformal mappings

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Abstract

A domain is called diametrically symmetric if it contains with each point its antipodal point on the Riemann sphere. We derive a variational formula for schlicht conformal mappings of such domains onto domains of the same type. This gives an analogue of a classical variational formula of Duren and Schiffer, which is in some sense an “elliptic analogue” of the “hyperbolic case” of Duren and Schiffer.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06099, Halle (Saale), Germany

    Reiner Kühnau

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  1. Reiner Kühnau
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Correspondence to Reiner Kühnau.

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Kühnau, R. Variation of diametrically symmetric or elliptically schlicht conformal mappings. J. Anal. Math. 89, 303–316 (2003). https://doi.org/10.1007/BF02893085

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  • DOI: https://doi.org/10.1007/BF02893085

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