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Comptes Rendus. Mathématique
Complex analysis and geometry
Quasiconformal extension for harmonic mappings on finitely connected domains
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 905-909.

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.

Received:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.233
Classification: 30C55,  30C62,  31A05
Iason Efraimidis 1

1. Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, United States.
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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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