Maximal dilatation ($K(f)=\frac{1+\Vert {\mu }_f{\Vert }_{\infty }}{1-\Vert {\mu }_f{\Vert }_{\infty }}$)

The essential supremum of the ratio of the largest to the smallest infinitesimal singular value of a quasiconformal map. It equals $(1+\Vert {\mu }_f{\Vert }_{\infty })/(1-\Vert {\mu }_f{\Vert }_{\infty })$ in terms of the Beltrami coefficient.