Samuel Krushkal

Beyond Moser's Conjecture on Grunsky Inequalities

We prove a weakened version of a conjecture concerning the relation between the Grunsky constant and the Teichm\"{u}ller norm of extensions of univalent functions.

Quasiconformal extension, univalent function, Grunsky coefficient inequalities, asymptotically conformal curve, universal Teichm\"{u}ller space, subharmonic Finsler metrics, Fredholm eigenvalues, Minda's maximum principle.

MSC 2000: Primary: 30C35, 30C62. Secondary: 30F60, 32F45