Ahlfors-Weill extensions for harmonic mappings
Iason Efraimidis, Rodrigo Hern\'andez, Mar\'ia J. Mart\'in
TL;DR
This paper introduces two new formulas for extending harmonic mappings from the unit disk to the entire complex plane, generalizing the Ahlfors-Weill extension for holomorphic functions, under conditions of small Schwarzian derivative.
Contribution
It provides novel formulas for quasiconformal extensions of harmonic mappings, extending classical results to a broader class of functions with small Schwarzian derivative.
Findings
Two new formulas for harmonic extension are derived.
Extensions are quasiconformal and generalize Ahlfors-Weill for holomorphic functions.
Applicable to harmonic mappings with sufficiently small Schwarzian derivative.
Abstract
We provide two new formulas for quasiconformal extension to for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions.
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Taxonomy
TopicsAnalytic and geometric function theory · Pelvic and Acetabular Injuries