The growth and 1∕4-theorems for starlike mappings in Cⁿ

Roger W. Barnard, Carl Hanson Fitzgerald and Sheng Gong

Vol. 150 (1991), No. 1, 13–22

DOI: 10.2140/pjm.1991.150.13

Abstract

Certain geometric function theory results are obtained for holomorphic mappings on the unit ball. Specifically, the mappings studied are one-to-one onto domains that are starlike with respect to the origin. For such a mapping f(z), sharp estimates are derived for |f(z)| in terms of |z|. Also, a generalization of the Koebe covering theorem is proved. As a corollary of the work, a new proof is given that, in Cⁿ for n ≥ 2, a ball and a polydisc are not biholomorphically equivalent.

Mathematical Subject Classification 2000

Primary: 32H02

Milestones

Received: 20 March 1989

Published: 1 September 1991