Georgian Mathematical Journal 13 (2006), No. 3, 495--500
Copyright Heldermann Verlag 2006
Inversion of Ahlfors and Grunsky Inequalities
Samuel Krushkal
Dept. of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
and: Dept. of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
skrushkl@memphis.edu
We solve the old Kühnau'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: 30C35, 30C62, 30F45; 30F60, 31A10, 53A35
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