平面调和映射的Schwarz导数与对数导数的新定义  

New definitions of Pre-Schwarzian and Schwarzian derivatives of harmonic mappings in the plane

作　　者：谭俊键 张琴 冯小高[1] Tan Junjian;Zhang qin;Feng Xiaogao(College of Mathematics and Information,China West Normal University,Nanchong 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

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).

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.

关 键 词：SCHWARZ导数 对数导数 调和映射 

分 类 号：O178[理学—数学]