Ahlfors-Weill extensions for harmonic mappings

Iason Efraimidis; Rodrigo Hernández; María J. Martín

Ahlfors-Weill extensions for harmonic mappings

Complex Variables 2021-05-18 v1

Authors: Iason Efraimidis , Rodrigo Hernández , María J. Martín

Abstract

We provide two new formulas for quasiconformal extension to $\overline{\mathbb{C}}$ 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.

Keywords

extension theorems holomorphic mappings harmonic functions

Cite

@article{arxiv.2105.07492,
  title  = {Ahlfors-Weill extensions for harmonic mappings},
  author = {Iason Efraimidis and Rodrigo Hernández and María J. Martín},
  journal= {arXiv preprint arXiv:2105.07492},
  year   = {2021}
}

Comments

14 pages

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