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