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QUASICONFORMAL EXTENSIONS OF HARMONIC MAPPINGS WITH A COMPLEX PARAMETER

Part of: Geometric function theory Two-dimensional theory

Published online by Cambridge University Press:  19 September 2016

XINGDI CHEN  and
YUQIN QUE
XINGDI CHEN*
Affiliation:
Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362021, PR China email chxtt@hqu.edu.cn
YUQIN QUE
Affiliation:
Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362021PR China email queyuqin@hqu.edu.cn
*
✉chxtt@hqu.edu.cn
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Abstract

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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.

Keywords

harmonic mappingTeichmüller mappingquasiconformal extensionharmonic quasiconformal mapping

MSC classification

Primary: 30C62: Quasiconformal mappings in the plane 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C55: General theory of univalent and multivalent functions
Secondary: 31A05: Harmonic, subharmonic, superharmonic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 3 , June 2017 , pp. 307 - 315
Copyright
© 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).

References

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