复微分算子下调和映照的单叶半径

数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 171-178.

复微分算子下调和映照的单叶半径

朱剑峰|黄心中

华侨大学数学科学学院福建泉州 362021

收稿日期:2012-06-10 修回日期:2013-05-15 出版日期:2014-02-25 发布日期:2014-02-25
基金资助:
华侨大学侨办基金资助项目(10QZR22)和国家自然科学基金项目(11101165)资助.

The Univalent Radius of Harmonic Mappings Under Complex-Operator

ZHU Jian-Feng, HUANG Xin-Zhong

School of Mathematical Sciences, Huaqiao University, Fujian Quanzhou 362021

Received:2012-06-10 Revised:2013-05-15 Online:2014-02-25 Published:2014-02-25
Supported by:
华侨大学侨办基金资助项目(10QZR22)和国家自然科学基金项目(11101165)资助.

摘要/Abstract

摘要：

设f(z)为定义在单位圆盘D上的调和映照, 定义复微分算子L:=z∂/∂z-z∂/∂z. 该文在f满足系数条件(1.7)下, 得到L(f)的单叶半径ρ₀如(1.9)式. 进而当f为调和K -拟共形映照时, 得到L(f)的单叶半径ρ_K.

关键词: 调和映照, 拟共形映照, Bloch常数, Landau定理, 复微分算子

Abstract:

Assume f(z) is a harmonic mapping defined in the unit disk D, denote complex-operator L:=z∂/∂z-z∂/∂z. In this paper, assume f satisfys coefficient condition (1.7), we obtained the univalent radius ρ₀of L(f). Here ρ₀ is defined by (1.9). Moreover, if f is a harmonic K-quasiconformal mapping, we also obtained the univalent radium ρ_K of L(f).

Key words: Harmonic mapping, quasiconformal mapping, Bloch constant, Landau theorem, Complex-operator

中图分类号:

30C75

朱剑峰, 黄心中. 复微分算子下调和映照的单叶半径[J]. 数学物理学报, 2014, 34(1): 171-178.

ZHU Jian-Feng, HUANG Xin-Zhong. The Univalent Radius of Harmonic Mappings Under Complex-Operator[J]. Acta mathematica scientia,Series A, 2014, 34(1): 171-178.