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arXiv · 2101.09561

Quasiconformal extension for harmonic mappings on finitely connected domains

Iason Efraimidis
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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.

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Iason Efraimidis. 2021-01-23. Quasiconformal extension for harmonic mappings on finitely connected domains. https://arxiv.org/abs/2101.09561

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