An elementary proof of a theorem concerning infinitely connected domains

Author:
R. J. Sibner

Journal:
Proc. Amer. Math. Soc. **37** (1973), 459-461

MSC:
Primary 30A30

MathSciNet review:
0310215

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**Zeev Nehari,*Conformal mapping*, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1952. MR**0045823****[2]**R. J. Sibner,*Domains bounded by analytic Jordan curves*, Bull. Amer. Math. Soc.**76**(1970), 61–63. MR**0255785**, 10.1090/S0002-9904-1970-12366-7**[3]**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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
30A30

Retrieve articles in all journals with MSC: 30A30

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0310215-2

Keywords:
Conformal mapping,
infinitely connected domains,
analytic Jordan curves

Article copyright:
© Copyright 1973
American Mathematical Society