QUASICONFORMAL EXTENSIONS OF HARMONIC MAPPINGS WITH A COMPLEX PARAMETER

被引：4

作者：

Chen, Xingdi ^{[1
]}

Que, Yuqin ^{[1
]}

机构：

[1] Huaqiao Univ, Dept Math, Quanzhou 362021, Fujian, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 102卷 / 03期

关键词：

harmonic mapping; Teichmuller mapping; quasiconformal extension; harmonic quasiconformal mapping; SCHWARZIAN;

D O I：

10.1017/S1446788716000355

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Hernandez and Martin ['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 Teichmuller mapping, whose maximal dilatation estimate is asymptotically sharp.

引用

页码：307 / 315

页数：9

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