A proof of the uniformization theorem for arbitrary plane domains
HTML articles powered by AMS MathViewer
- by Yuval Fisher, John H. Hubbard and Ben S. Wittner PDF
- Proc. Amer. Math. Soc. 104 (1988), 413-418 Request permission
Abstract:
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe’s constructive proof of the Riemann mapping theorem, and the resulting algorithm can be used to estimate the Poincaré metric for the domain.References
- Lars V. Ahlfors, Complex analysis, 3rd ed., International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable. MR 510197
- Paul Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 85–141. MR 741725, DOI 10.1090/S0273-0979-1984-15240-6
- Otto Forster, Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, New York-Berlin, 1981. Translated from the German by Bruce Gilligan. MR 648106
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 413-418
- MSC: Primary 30F10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0962807-6
- MathSciNet review: 962807