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Univalent functions and the Riemann mapping theorem


Author: P. R. Garabedian
Journal: Proc. Amer. Math. Soc. 61 (1976), 242-244
MSC: Primary 30A30
DOI: https://doi.org/10.1090/S0002-9939-1976-0425094-5
MathSciNet review: 0425094
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Abstract: A proof of the Riemann mapping theorem is given that depends on variational formulas for univalent functions. The method of proof can be used to simplify the derivation of the ordinary differential equation for extremal univalent functions given by Schiffer in 1938.

References [Enhancements On Off] (What's this?)

  • [1] R. de Possel, Zum Parallelschlitztheorem unendlich-vielfach zusammenhaengender Gebiete, Nachr. Ges. Wiss. Goettingen Math. Phys. Kl. (1) 23 (1931), 199-202.
  • [2] M. Schiffer, A method of variation within the family of simple functions, Proc. London Math. Soc. 44 (1938), 432-449.

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DOI: https://doi.org/10.1090/S0002-9939-1976-0425094-5
Article copyright: © Copyright 1976 American Mathematical Society