Comptes Rendus. Mathématique (Sep 2021)

Quasiconformal extension for harmonic mappings on finitely connected domains

  • Efraimidis, Iason

DOI
https://doi.org/10.5802/crmath.233
Journal volume & issue
Vol. 359, no. 7
pp. 905 – 909

Abstract

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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.