Teichmüller map
= Teichmüller map
{c}
{title2=$\mu=k|q|/q$}
A <quasiconformal map> whose <Beltrami coefficient> is $k|q|/q$ for an integrable nonzero <holomorphic quadratic differential> and constant $0<k<1$. In a <flat coordinate> for $q$, it stretches the horizontal and vertical directions with ratio $K=(1+k)/(1-k)$. Positive multiples of $q$ define the same coefficient.