An elementary proof of a theorem concerning infinitely connected domains
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- by R. J. Sibner PDF
- Proc. Amer. Math. Soc. 37 (1973), 459-461 Request permission
Abstract:
Using classical complex function theory, it is shown that any infinitely connected plane domain is conformally equivalent to a domain whose isolated boundary components are analytic Jordan curves. This allows an elementary proof to be given of the result that a domain with countably many boundary components is conformally equivalent to a domain bounded by analytic Jordan curves.References
- Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
- R. J. Sibner, Domains bounded by analytic Jordan curves, Bull. Amer. Math. Soc. 76 (1970), 61–63. MR 255785, DOI 10.1090/S0002-9904-1970-12366-7
- R. J. Sibner, “Uniformizations” of indefinitely connected domains, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 407–420. MR 0288256
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 459-461
- MSC: Primary 30A30
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310215-2
- MathSciNet review: 0310215