Distortion theorems for locally univalent Bloch functions (Q2565375)

A holomorphic function defined on the unit disk \(D\) is called a Bloch function if \[ |f|_B= \sup\biggl \{\bigl(1- |z |^2 \bigr) \bigl|f'(z) \bigr|: z\in D\biggr\} <\infty. \] In this paper, for \(\alpha \in(0,1]\), the class of locally univalent Bloch functions \(f\) normalized by \(|f|_B\leq 1\), \(f(0)=0\) and \(f'(0)= \alpha\), denoted by \(B_\infty (\alpha)\), is studied. A type of subordination theorem is established. This subordination theorem is used to derive sharp growth, distortion, curvature and covering theorems for \(B_\infty (\alpha)\).