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

被引：20
|
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.
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页码：2327 / 2334
页数：8
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