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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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:

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.


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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
Email: jerry.muir@rose-hulman.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/S0002-9939-01-05967-6
PII: S 0002-9939(01)05967-6
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