Let $f$ be an holomorphic function on a region containing the closure of the disk $D=\{z\in\mathbb{C}:|z|<1\}$ such that $f(0)=0$ and $f'(0)=1$ Then there is a disk $S\subset D$ such that $f$ is injective on $S$ and $f(S)$contains a disk of radius$\frac{1}{72}$
32H02 (Several complex variables and analytic spaces :: Holomorphic mappings and correspondences :: Holomorphic mappings, embeddings and related questions)
