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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A generalization of half-plane mappings to the ball in $ \mathbb{C}^n$


Authors: Jerry R. Muir Jr. and Ted J. Suffridge
Journal: Trans. Amer. Math. Soc. 359 (2007), 1485-1498
MSC (2000): Primary 32H02; Secondary 30C55.
Published electronically: November 3, 2006
MathSciNet review: 2272135
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Abstract: Let $ F$ be a normalized ($ F(0)=0$, $ DF(0)=I$) biholomorphic mapping of the unit ball $ B \subseteq \mathbb{C}^n$ onto a convex domain $ \Omega \subseteq \mathbb{C}^n$ that is the union of lines parallel to some unit vector $ u \in \mathbb{C}^n$. We consider the situation in which there is one infinite singularity of $ F$ on $ \partial B$. In one case with a simple change-of-variables, we classify all convex mappings of $ B$ that are half-plane mappings in the first coordinate. In the more complicated case, when $ u$ is not in the span of the infinite singularity, we derive a form of the mappings in dimension $ n=2$.


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Additional Information

Jerry R. Muir Jr.
Affiliation: Department of Mathematics, University of Scranton, Scranton, Pennsylvania 18510
Email: muirj2@scranton.edu

Ted J. Suffridge
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: ted@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04205-X
PII: S 0002-9947(06)04205-X
Keywords: Biholomorphic, convex mapping, holomorphic automorphism.
Received by editor(s): January 4, 2005
Published electronically: November 3, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.