Quasiconformal extension for harmonic mappings on finitely connected domains
Complex Variables
2021-02-05 v2
Abstract
We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian derivative is small. We also make the observation that a univalence criterion for harmonic mappings holds on uniform domains.
Keywords
Cite
@article{arxiv.2101.09561,
title = {Quasiconformal extension for harmonic mappings on finitely connected domains},
author = {Iason Efraimidis},
journal= {arXiv preprint arXiv:2101.09561},
year = {2021}
}
Comments
6 pages, 1 figure; slightly extended introduction in version 2