# Bloch’s theorem

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 $f^{\prime}(0)=1$. Then there is a disk $S\subset D$ such that $f$ is injective on $S$ and $f(S)$ contains a disk of radius $\frac{1}{72}$.

Title Bloch’s theorem BlochsTheorem 2013-03-22 13:15:17 2013-03-22 13:15:17 Koro (127) Koro (127) 5 Koro (127) Theorem msc 32H02