The Schwarz-Pick lemma and Julia lemma for real planar harmonic mappings

被引：21

作者：

Chen HuaiHui ^{[1
]}

机构：

[1] Nanjing Normal Univ, Dept Math, Nanjing 210097, Jiangsu, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 11期

基金：

中国国家自然科学基金;

关键词：

harmonic mappings; Schwarz-Pick lemma; Julia lemma;

D O I：

10.1007/s11425-013-4691-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The classical Schwarz-Pick lemma and Julia lemma for holomorphic mappings on the unit disk D are generalized to real harmonic mappings of the unit disk, and the results are precise. It is proved that for a harmonic mapping U of D into the open interval I = (-1, 1), holds for z a D, where I > (U) (z) is the maximum dilation of U at z. The inequality is sharp for any z a D and any value of U(z), and the equality occurs for some point in D if and only if , z a D, with a Mobius transformation phi of D onto itself.

引用

页码：2327 / 2334

页数：8