Unbounded convex mappings of the ball in $\mathbb {C}^n$
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- by Jerry R. Muir Jr. and Ted J. Suffridge PDF
- Proc. Amer. Math. Soc. 129 (2001), 3389-3393 Request permission
Abstract:
In this paper, we study univalent holomorphic mappings of the unit ball in $\mathbb {C}^n$ that have the property that the image $F(B)$ contains a line $\{tu: t \in \mathbb {R} \}$ for some $u \in \mathbb {C}^n$, $u \neq 0$. We show that under certain rather reasonable conditions, up to composition with a holomorphic automorphism of the ball, the mapping $F$ is an extension of the strip mapping in the plane to higher dimensions.References
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- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
Additional Information
- Jerry R. Muir Jr.
- Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, 5500 Wabash Ave., Terre Haute, Indiana 47803
- Email: jerry.muir@rose-hulman.edu
- Ted J. Suffridge
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
- Email: ted@ms.uky.edu
- Received by editor(s): March 9, 2000
- Received by editor(s) in revised form: April 7, 2000
- Published electronically: April 24, 2001
- Communicated by: Steven R. Bell
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3389-3393
- MSC (1991): Primary 32H02; Secondary 30C55
- DOI: https://doi.org/10.1090/S0002-9939-01-05967-6
- MathSciNet review: 1845017