We present a simplified version of the de Branges proof of the Lebedev-Milin conjecture which implies the Robertson and Bieberbach conjectures. As an application of an analysis of the technique, it is shown that the method could not be used directly to prove the Bieberbach conjecture.
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.
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