Convexity properties of holomorphic mappings in $\mathbb {C}^n$
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- by Kevin A. Roper and Ted J. Suffridge PDF
- Trans. Amer. Math. Soc. 351 (1999), 1803-1833 Request permission
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.References
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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
- Received by editor(s): July 10, 1995
- Received by editor(s) in revised form: August 11, 1997
- Published electronically: January 26, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 1803-1833
- MSC (1991): Primary 32H99; Secondary 30C45
- DOI: https://doi.org/10.1090/S0002-9947-99-02219-9
- MathSciNet review: 1475692