Parametrization of domains in : 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 -fold connected domain in , 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.

**[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****[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****[3]**Lawrence Zalcmann,*Analytic capacity and rational approximation*, Lecture Notes in Mathematics, No. 50, Springer-Verlag, Berlin-New York, 1968. MR**0227434**

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1990-0974521-5

Article copyright:
© Copyright 1990
American Mathematical Society