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QUASICONFORMAL EXTENSIONS OF HARMONIC MAPPINGS WITH A COMPLEX PARAMETER
Published online by Cambridge University Press: 19 September 2016
Abstract
In this paper, we study quasiconformal extensions of harmonic mappings. Utilizing a complex parameter, we build a bridge between the quasiconformal extension theorem for locally analytic functions given by Ahlfors [‘Sufficient conditions for quasiconformal extension’, Ann. of Math. Stud.79 (1974), 23–29] and the one for harmonic mappings recently given by Hernández and Martín [‘Quasiconformal extension of harmonic mappings in the plane’, Ann. Acad. Sci. Fenn. Math.38 (2) (2013), 617–630]. We also give a quasiconformal extension of a harmonic Teichmüller mapping, whose maximal dilatation estimate is asymptotically sharp.
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- Research Article
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- © 2016 Australian Mathematical Publishing Association Inc.
Footnotes
This paper is supported by NNSF of China (11471128), the Natural Science Foundation of Fujian Province of China (2014J01013), NCETFJ Fund (2012FJ-NCET-ZR05), Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-YX110).
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