Some Liouville-type theorems for harmonic functions on Finsler manifolds

被引：18
|
作者：
Zhang, Fu-e [1 ,2 ]
Xia, Qiaoling [1 ]
机构：
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[2] Shihezi Univ, Dept Math, Shihezi 832003, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 417卷 / 02期
关键词：
Finsler Laplacian; Liouville-type theorem; Harmonic function; METRIC-MEASURE-SPACES; GEOMETRY; RECURRENCE;
D O I：
10.1016/j.jmaa.2014.03.078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give some Liouville-type theorems for L-p (p is an element of R) harmonic (resp. subharmonic, superharmonic) functions on forward complete Finsler manifolds. Moreover, we derive a gradient estimate for harmonic functions on a closed Finsler manifold. As an application, one obtains that any harmonic function on a closed Finsler manifold with nonnegative weighted Ricci curvature Ric(N) (N is an element of (n, infinity)) must be constant. (C) 2014 Elsevier Inc. All rights reserved.
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页码：979 / 995
页数：17
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