A note on the ρ-Nitsche conjecture

被引：0
|
作者：
Feng, Xiaogao [1 ,2 ]
Tang, Shuan [3 ]
机构：
[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China
[2] China West Normal Univ, Coll Math & Informat, Nanchong 637002, Peoples R China
[3] Guizhou Normal Univ, Dept Math, Guiyang 550001, Peoples R China
来源：
ARCHIV DER MATHEMATIK | 2016年 / 107卷 / 01期
基金：
中国国家自然科学基金;
关键词：
rho-Nitsche conjecture; Nitsche conjecture; Harmonic mapping; rho-Harmonic mapping; UNIVALENT HARMONIC-MAPPINGS; MEAN DISTORTION; ANNULI; DEFORMATIONS; SURFACES;
D O I：
10.1007/s00013-016-0906-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let be a radial symmetric Riemannian metric defined in the annulus A(1, R). Kalaj conjectured that if there exists a -harmonic homeomorphism from the annulus A(1, r) onto A(1, R), then R satisfies the following -Nitsche condition In this note, we prove that if , then there exists a -harmonic mapping between A(1, r) and A(1, R) if and only if , i.e. the -Nitsche condition holds. This gives a positive answer to Kalaj's conjecture for . Some related topics are also discussed.
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页码：81 / 88
页数：8
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