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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

Masahiko Taniguchi
Affiliation: Department of Mathematics, Graduate school of Science, Kyoto University, Kyoto 606, Japan

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