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.
Accepted:
Published online:
DOI: 10.5802/crmath.233
Iason Efraimidis 1
@article{CRMATH_2021__359_7_905_0, author = {Iason Efraimidis}, title = {Quasiconformal extension for harmonic mappings on finitely connected domains}, journal = {Comptes Rendus. Math\'ematique}, pages = {905--909}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {7}, year = {2021}, doi = {10.5802/crmath.233}, zbl = {07398742}, language = {en}, }
Iason Efraimidis. Quasiconformal extension for harmonic mappings on finitely connected domains. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 905-909. doi : 10.5802/crmath.233. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.233/
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