A generalization of half-plane mappings to the ball in $\mathbb {C}^n$
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- by Jerry R. Muir Jr. and Ted J. Suffridge PDF
- Trans. Amer. Math. Soc. 359 (2007), 1485-1498 Request permission
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 $n=2$.References
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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
- Received by editor(s): January 4, 2005
- Published electronically: November 3, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 1485-1498
- MSC (2000): Primary 32H02; Secondary 30C55
- DOI: https://doi.org/10.1090/S0002-9947-06-04205-X
- MathSciNet review: 2272135