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Complex Variables and Elliptic Equations
An International Journal
Volume 52, 2007 - Issue 2-3: A tribute to Peter Duren
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Original Articles

Growth and two-point distortion for biholomorphic mappings of the ball

Ian Graham Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
,
Gabriela Kohr Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogǎalniceanu Str., 400084 Cluj-Napoca, Romania
&
John Pfaltzgraff Department of Mathematics, CB 3250, University of North Carolina>, Chapel Hill, NC 27599-3250, USACorrespondence[email protected]
Pages 211-223 | Received 13 Jun 2006, Accepted 20 Aug 2006, Published online: 19 Oct 2007
 
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Abstract

In this article we obtain invariant two-point distortion theorems for univalent holomorphic mappings of the unit ball in one and in several variables. A new locally uniform minimum growth bound for biholomorphic mappings of the unit ball in dimension n>1 is obtained for those mappings with finite “norm order”. The results are framed in the context of linear invariant families and the Koebe transform.

¶Dedicated to Professor Peter L. Duren on the occasion of his 70th birthday

Acknowledgement

The authors thank the referee for a very careful reading of the article and for stimulating suggestions.

Notes

¶Dedicated to Professor Peter L. Duren on the occasion of his 70th birthday

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