On the Extremality of Harmonic Beltrami Coefficients

On the Extremality of Harmonic Beltrami Coefficients

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...

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Bibliographic Details
Main Author: Samuel L. Krushkal
Format: Article
Language:English
Published: MDPI AG 2022-07-01
Series:Mathematics
Subjects:
univalent function
Grunsky operator
quasiconformal extension
harmonic Beltrami coefficients
quasireflections
universal Teichmüller space
Online Access:https://www.mdpi.com/2227-7390/10/14/2460
Description
Summary: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.
ISSN:2227-7390

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