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arXiv · 2112.13653

On quasiconformal extensions of harmonic mappings associated with pre-Schwarzian derivative

Xiao-Yuan Wang·Jin-Hua Fan·Zhen-Yong Hu·Zhi-Gang Wang
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Abstract

In this paper, we extend Ahlfors's univalent criteria and Ahlfors's quasiconformal extension for analytic functions to harmonic mappings defined in the unit disk. Moreover, we give a general quasiconformal extension of harmonic Teichm\"{u}ller mappings, whose maximal dilatation estimate is asymptotically sharp.

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Xiao-Yuan Wang, Jin-Hua Fan, Zhen-Yong Hu, Zhi-Gang Wang. 2021-12-27. On quasiconformal extensions of harmonic mappings associated with pre-Schwarzian derivative. https://arxiv.org/abs/2112.13653

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