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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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, American Mathematical Society Colloquium Publications, Vol. 34, American Mathematical Society, New York, N. Y., 1950. MR 0037350 (12,249d)
  • [2] J. L. Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society Colloquium Publications, Vol. 34, American Mathematical Society, New York, N. Y., 1950. MR 0037350 (12,249d)
  • [3] Lawrence Zalcmann, Analytic capacity and rational approximation, Lecture Notes in Mathematics, No. 50, Springer-Verlag, Berlin-New York, 1968. MR 0227434 (37 #3018)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0974521-5
PII: S 0002-9947(1990)0974521-5
Article copyright: © Copyright 1990 American Mathematical Society