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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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