Samuel Krushkal

Inversion of Ahlfors and Grunsky Inequalities

Abstract:
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.

Keywords:
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.