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Transactions of the American Mathematical Society

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Parametrization of domains in $ \hat{\bf C}$: the logarithmic domains


Authors: Johannes Michaliček and Rodolfo Wehrhahn
Journal: Trans. Amer. Math. Soc. 320 (1990), 765-777
MSC: Primary 30C20; Secondary 30C35, 31A99
DOI: https://doi.org/10.1090/S0002-9947-1990-0974521-5
MathSciNet review: 974521
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Abstract: We prove a generalization of Riemann's mapping theorem: Every $ n$-fold connected domain in $ \widehat{\mathbf{C}}$, whose boundary does not contain isolated points, is conformal equivalent to a logarithmic domain. The logarithmic domains are characterized by a Green's function consisting of a finite sum of logarithms.


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

  • [1] J. L. Walsh, The location of critical points of analytic and harmonic functions, Amer. Math. Soc. Colloq. Publ., vol. 34, Amer. Math. Soc., Providence, R.I., 1950, p. 248, Theorem 2. MR 0037350 (12:249d)
  • [2] -, The location of critical points of analytic and harmonic functions, Amer. Math. Soc. Colloq. Publ., vol. 34, Amer. Math. Soc., Providence, R.I., 1950. MR 0037350 (12:249d)
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DOI: https://doi.org/10.1090/S0002-9947-1990-0974521-5
Article copyright: © Copyright 1990 American Mathematical Society

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