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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Convexity properties
of holomorphic mappings in ${\mathbb C}^n$


Authors: Kevin A. Roper and Ted J. Suffridge
Journal: Trans. Amer. Math. Soc. 351 (1999), 1803-1833
MSC (1991): Primary 32H99; Secondary 30C45
Published electronically: January 26, 1999
MathSciNet review: 1475692
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Abstract: Not many convex mappings on the unit ball in ${\mathbb C}^n$ for $n>1$ are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the ``Quasi-Convex Mappings, Types A and B'' seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the convex mappings.


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Additional Information

Kevin A. Roper
Affiliation: Department of Mathematics, Munro College, P.O., St. Elizabeth, Jamaica

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/S0002-9947-99-02219-9
PII: S 0002-9947(99)02219-9
Keywords: Convex, holomorphic mapping, dimension $n$
Received by editor(s): July 10, 1995
Received by editor(s) in revised form: August 11, 1997
Published electronically: January 26, 1999
Article copyright: © Copyright 1999 American Mathematical Society