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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Boundary behaviour of level curves of harmonic functions
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by W. J. Walker PDF
Proc. Amer. Math. Soc. 91 (1984), 102-104 Request permission

Abstract:

Sufficient conditions are obtained for a function harmonic in the disk and continuous at a boundary point to have a level curve emanating from the boundary point into the disk. The one-sided derivative of the level curve is studied at the boundary point.
References
    N. K. Bary, A treatise on trigonometric series, Vol. I, Pergamon Press, New York and Oxford, 1964.
  • John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
  • Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 102-104
  • MSC: Primary 31A05
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0735573-3
  • MathSciNet review: 735573