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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bell representations of finitely connected planar domains


Authors: Moonja Jeong and Masahiko Taniguchi
Journal: Proc. Amer. Math. Soc. 131 (2003), 2325-2328
MSC (2000): Primary 32G10, 32G15; Secondary 30C20, 30F60
Published electronically: November 14, 2002
MathSciNet review: 1974628
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Abstract: In this paper, we solve a conjecture of S. Bell (1992) affirmatively. Actually, we prove that every non-degenerate $n$-connected planar domain $\Omega$, where $n>1$is representable as $\Omega= \{\vert f\vert<1\}$with a suitable rational function $f$of degree $n$. This result is considered as a natural generalization of the classical Riemann mapping theorem for simply connected planar domains.


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Additional Information

Moonja Jeong
Affiliation: Department of Mathematics, The University of Suwon, Suwon P.O. Box 77, Kyung- kido, 440-600, Korea
Email: mjeong@mail.suwon.ac.kr

Masahiko Taniguchi
Affiliation: Department of Mathematics, Graduate school of Science, Kyoto University, Kyoto 606, Japan
Email: tanig@kusm.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06823-5
PII: S 0002-9939(02)06823-5
Keywords: Conformal representation, Ahlfors maps
Received by editor(s): March 15, 2002
Published electronically: November 14, 2002
Additional Notes: The second author was supported in part by Grant-in-Aid for Scientific Research (B)(2) 2001-13440047.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2002 American Mathematical Society