Automorphism of the unit disk
= Automorphism of the unit disk
{title2=$\phi(z)=e^{i\theta}\frac{z-a}{1-\overline a z}$}
= Automorphisms of the unit disk
{synonym}
A <biholomorphism> of the unit disk to itself. Every such map has the form $e^{i\theta}(z-a)/(1-\overline a z)$ with $|a|<1$. These maps normalize an extremal <univalent function> in the proof of the <Riemann mapping theorem>.