Generalized harmonic functions of Riemannian manifolds with ends

被引：0
|
作者：
S. A. Korolkov
A. G. Losev
机构：
[1] Volgograd State University,Department of Mathematics and Information Technology
来源：
Mathematische Zeitschrift | 2012年 / 272卷
关键词：
Liouville theorem; Riemannian manifold; -harmonic function; Boundary problems for ; -harmonic functions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study L-harmonic functions (solutions of the stationary Schrödinger equation) on arbitrary noncompact Riemannian manifolds with finitely many ends. We establish some existence and uniqueness results, and obtain sharp dimension estimates for L-harmonic functions on such manifolds.
引用
下载
收藏
页码：459 / 472
页数：13
相关论文
共 50 条
  • [41] Geometric characterization of level set families of harmonic functions on Riemannian manifolds
    Lin, Cunda
    [J]. JOURNAL OF ANALYSIS, 2024, 32 (02): : 787 - 794
  • [42] Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary
    Jiang, Xinrong
    Mao, Jianyi
    [J]. MANUSCRIPTA MATHEMATICA, 2024, 174 (3-4) : 1103 - 1112
  • [43] Polynomial growth harmonic functions on connected sums of complete Riemannian manifolds
    Kim, SW
    Lee, YH
    [J]. MATHEMATISCHE ZEITSCHRIFT, 2000, 233 (01) : 103 - 113
  • [44] Local gradient estimate for p-harmonic functions on Riemannian manifolds
    Wang, Xiaodong
    Zhang, Lei
    [J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2011, 19 (04) : 759 - 771
  • [45] ON COMPLETE RIEMANNIAN-MANIFOLDS WITH COLLAPSED ENDS
    SHEN, ZM
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 1994, 163 (01) : 175 - 182
  • [46] On generalized recurrent Riemannian manifolds
    Arslan, K.
    De, U. C.
    Murathan, C.
    Yildiz, A.
    [J]. ACTA MATHEMATICA HUNGARICA, 2009, 123 (1-2) : 27 - 39
  • [47] ON GENERALIZED SEMISYMMETRIC RIEMANNIAN MANIFOLDS
    Mikes, Josef
    Stepanov, Sergey E.
    [J]. ATTI ACCADEMIA PELORITANA DEI PERICOLANTI-CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI, 2013, 91
  • [48] On generalized recurrent Riemannian manifolds
    Singh, H
    Khan, Q
    [J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2000, 56 (1-2): : 87 - 95
  • [49] On generalized recurrent Riemannian manifolds
    K. Arslan
    U. C. De
    C. Murathan
    A. Yildiz
    [J]. Acta Mathematica Hungarica, 2009, 123 : 27 - 39
  • [50] On Geodesic Convex and Generalized Geodesic Convex Functions over Riemannian Manifolds
    Shahi, Avanish
    Mishra, S. K.
    [J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON FRONTIERS IN INDUSTRIAL AND APPLIED MATHEMATICS (FIAM-2018), 2018, 1975
12345