Vol. 150, No. 1, 1991

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ISSN: 0030-8730
The growth and 14-theorems for starlike mappings in Cn

Roger W. Barnard, Carl Hanson Fitzgerald and Sheng Gong

Vol. 150 (1991), No. 1, 13–22

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
Received: 20 March 1989
Published: 1 September 1991
Roger W. Barnard
Carl Hanson Fitzgerald
Sheng Gong