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

Complex Variables 2021-12-28 v1

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.

Keywords

Cite

@article{arxiv.2112.13653,
  title  = {On quasiconformal extensions of harmonic mappings associated with pre-Schwarzian derivative},
  author = {Xiao-Yuan Wang and Jin-Hua Fan and Zhen-Yong Hu and Zhi-Gang Wang},
  journal= {arXiv preprint arXiv:2112.13653},
  year   = {2021}
}

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17 pages