On the Extremality of Harmonic Beltrami Coefficients

Abstract

We prove a general theorem, which provides a broad collection of univalent functions with equal Grunsky and Teichmüller norms and thereby the Fredholm eigenvalues and the reflection coefficients of associated quasicircles. It concerns an important problem to establish the exact or approximate values of basic quasiinvariant functionals of Jordan curves, which is crucial in applications and in the numerical aspect of quasiconformal analysis.

Keywords

• univalent function
• Grunsky operator
• quasiconformal extension
• harmonic Beltrami coefficients
• quasireflections
• universal Teichmüller space