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.
引用
收藏
页码：979 / 995
页数：17
相关论文
共 50 条
  • [31] LIOUVILLE THEOREMS FOR EXPONENTIALLY HARMONIC-FUNCTIONS ON RIEMANNIAN-MANIFOLDS
    HONG, MC
    MANUSCRIPTA MATHEMATICA, 1992, 77 (01) : 41 - 46
  • [32] Liouville-Type Theorems forCC-F-Harmonic Maps into a Carnot Group
    He, Guoqing
    Li, Jing
    Zhao, Peibiao
    JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (04) : 4024 - 4050
  • [33] Some symmetry results and Liouville-type theorems for solutions to semilinear equations
    Farina, Alberto
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 : 223 - 229
  • [34] Some rigidity theorems on Finsler manifolds
    Yin, Songting
    AIMS MATHEMATICS, 2021, 6 (03): : 3025 - 3036
  • [35] NONLINEAR LIOUVILLE-TYPE THEOREMS FOR GENERALIZED BAOUENDI-GRUSHIN OPERATOR ON RIEMANNIAN MANIFOLDS
    Jleli, Mohamed
    Ragusa, Maria Alessandra
    Samet, Bessem
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2023, 28 (1-2) : 143 - 168
  • [36] Liouville-type theorems for polyhannonic systems in RN
    Liu, Jiaqun
    Guo, Yuxia
    Zhang, Yajing
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 225 (02) : 685 - 709
  • [37] LIOUVILLE-TYPE THEOREMS FOR SEMILINEAR ELLIPTIC SYSTEMS
    Zhang Zhengce
    Wang Weimin
    Li Kaitai
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2005, 18 (04): : 304 - 310
  • [38] COUNTER-EXAMPLES FOR LIOUVILLE-TYPE THEOREMS
    KUZMENKO, YT
    MOLCANOV, SA
    VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1979, (06): : 39 - 43
  • [39] Llocp Positivity Preservation and Liouville-Type Theorems
    Bisterzo, Andrea
    Farina, Alberto
    Pigola, Stefano
    JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (04)
  • [40] Liouville-type theorems for semilinear elliptic systems
    Wang, Weimin
    Hong, Li
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) : 5380 - 5391
12345