Samuel Krushkal

Inversion of Ahlfors and Grunsky Inequalities

We solve the old Khnau's problem on the exact lower bound in the inverse inequality estimating the dilatation of a univalent function by its Grunsky norm and in the related Ahlfors inequality for Fredholm eigenvalues.

Grunsky coefficient inequalities, Fredholm eigenvalues, quasiconformal reflection, subharmonic function, Strebel point, conformal metric, generalized Gaussian curvature.

MSC 2000: Primary: 30C35, 30C62, 30F45. Secondary: 30F60, 31A10, 53A35.