The growth and 1<i>∕</i>4-theorems for starlike mappings in C^<i>n</i>

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 C" for n > 2, a ball and a polydisc are not biholomorphically equivalent.