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Unbounded convex mappings of the ball in $\mathbb{C} ^n$

Authors: Jerry R. Muir Jr. and Ted J. Suffridge
Journal: Proc. Amer. Math. Soc. 129 (2001), 3389-3393
MSC (1991): Primary 32H02; Secondary 30C55.
Published electronically: April 24, 2001
MathSciNet review: 1845017
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Abstract | References | Similar Articles | Additional Information


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 [Enhancements On Off] (What's this?)

  • 1. B.D. MacCluer, Iterates of holomorphic self-maps of the open unit ball in $\mathbb{C} ^n$, Mich. Math. J., 30 (1983), pp. 97-106. MR 85c:32047a
  • 2. Kevin A. Roper and Ted J. Suffridge, Convex mappings on the unit ball of $\mathbb{C} ^n$, Journal D'Analyse Math., 65 (1995), pp. 333-347. MR 96m:32023
  • 3. W. Rudin, Function Theory in the Unit Ball of $\mathbb{C} ^n$, Springer-Verlag, New York, 1980. MR 82i:32002

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Additional Information

Jerry R. Muir Jr.
Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, 5500 Wabash Ave., Terre Haute, Indiana 47803

Ted J. Suffridge
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

Keywords: Biholomorphic, convex mapping, holomorphic automorphism.
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
Article copyright: © Copyright 2001 American Mathematical Society

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