摘要
借助能量密度|fz|−|fz|,对单连通区域上的局部单叶调和映射分别给出了Schwarz导数和对数导数新的定义.同时,运用其新的定义分别讨论了当f为调和函数时,f的Schwarz导数的解析性和当f的Schwarz导数为调和时,f的Schwarz导数的解析性.
In this paper,we give new definitions of Pre-Schwarzian and Schwarzian derivatives for locally univalent harmonic maps on a simply connected domain by means of energy functional|fz|−|fz|.Meanwhile,we use the new definitions to discuss the analytic properties of Schwarzian derivative of f when f is harmonic and the analytic properties of Schwarzian derivative of f when the Schwarzian derivative of f is harmonic respectively.
作者
谭俊键
张琴
冯小高
Tan Junjian;Zhang qin;Feng Xiaogao(College of Mathematics and Information,China West Normal University,Nanchong 637009,China)
出处
《纯粹数学与应用数学》
2021年第3期362-369,共8页
Pure and Applied Mathematics
基金
国家自然科学基金(11701459)
西华师范大学科研启动基金(17E088).
关键词
SCHWARZ导数
对数导数
调和映射
Schwarzian derivative
Pre-Schwarzian derivative
harmonic mapping
