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Proceedings of the American Mathematical Society

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Boundary behaviour of level curves of harmonic functions


Author: W. J. Walker
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
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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 [Enhancements On Off] (What's this?)

  • [1] N. K. Bary, A treatise on trigonometric series, Vol. I, Pergamon Press, New York and Oxford, 1964.
  • [2] 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
  • [3] Christian Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen; Studia Mathematica/Mathematische Lehrbücher, Band XXV. MR 0507768

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DOI: https://doi.org/10.1090/S0002-9939-1984-0735573-3
Article copyright: © Copyright 1984 American Mathematical Society