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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Univalent functions and the Riemann mapping theorem
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by P. R. Garabedian PDF
Proc. Amer. Math. Soc. 61 (1976), 242-244 Request permission

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
    R. de Possel, Zum Parallelschlitztheorem unendlich-vielfach zusammenhaengender Gebiete, Nachr. Ges. Wiss. Goettingen Math. Phys. Kl. (1) 23 (1931), 199-202. M. Schiffer, A method of variation within the family of simple functions, Proc. London Math. Soc. 44 (1938), 432-449.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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