Liouville theorems of subelliptic harmonic maps

被引：1
|
作者：
Gao, Liu [1 ]
Lu, Lingen [2 ]
Yang, Guilin [3 ]
机构：
[1] Jinhua Polytech, Normal Sch, Jinhua 321017, Zhejiang, Peoples R China
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[3] Shanghai Lixin Univ Accounting & Finance, Sch Stat & Math, Shanghai 201620, Peoples R China
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2022年 / 61卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Subelliptic harmonic map; Liouville theorem; Vanishing-type theorem; Sub-Riemannian manifold; Totally geodesic Riemannian foliation; HARNACK INEQUALITY; UNIQUENESS; OPERATORS;
D O I：
10.1007/s10455-021-09811-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we discuss two Liouville-type theorems for subelliptic harmonic maps from sub-Riemannian manifolds to Riemannian manifolds. One is the Dirichlet version which states that two subelliptic harmonic maps from a sub-Riemannian manifold with boundary to a regular ball must be same if their restrictions on boundary are same; it is generalized to complete noncompact domains as well. The other is the vanishing-type theorem for finite L p-energy subelliptic harmonic maps on complete noncompact totally geodesic Riemannian foliations which are special sub-Riemannian manifolds.
引用
收藏
页码：293 / 307
页数：15
相关论文
共 50 条
  • [1] Liouville theorems of subelliptic harmonic maps
    Liu Gao
    Lingen Lu
    Guilin Yang
    Annals of Global Analysis and Geometry, 2022, 61 : 293 - 307
  • [2] Uniqueness and Liouville Properties of Subelliptic Harmonic Maps with Potential
    Luo, Han
    Yang, Guilin
    RESULTS IN MATHEMATICS, 2024, 79 (08)
  • [3] On subelliptic harmonic maps with potential
    Dong, Yuxin
    Luo, Han
    Yu, Weike
    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2024, 65 (01)
  • [4] Eells-Sampson Type Theorems for Subelliptic Harmonic Maps from sub-Riemannian Manifolds
    Dong, Yuxin
    JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (04) : 3608 - 3655
  • [5] Monotonicity formulae and Liouville theorems of harmonic maps with potential
    Lin, Hezi
    Yang, Guilin
    Ren, Yibin
    Chong, Tian
    JOURNAL OF GEOMETRY AND PHYSICS, 2012, 62 (09) : 1939 - 1948
  • [6] Liouville Theorems for F-Harmonic Maps and Their Applications
    Dong, Yuxin
    Lin, Hezi
    Yang, Guilin
    RESULTS IN MATHEMATICS, 2016, 69 (1-2) : 105 - 127
  • [7] Liouville Theorems for F-Harmonic Maps and Their Applications
    Yuxin Dong
    Hezi Lin
    Guilin Yang
    Results in Mathematics, 2016, 69 : 105 - 127
  • [8] Eells–Sampson Type Theorems for Subelliptic Harmonic Maps from sub-Riemannian Manifolds
    Yuxin Dong
    The Journal of Geometric Analysis, 2021, 31 : 3608 - 3655
  • [9] On subelliptic harmonic maps with potential
    Yuxin Dong
    Han Luo
    Weike Yu
    Annals of Global Analysis and Geometry, 2024, 65
  • [10] A stochastic approach to a priori estimates and Liouville theorems for harmonic maps
    Thalmaier, Anton
    Wang, Feng-Yu
    BULLETIN DES SCIENCES MATHEMATIQUES, 2011, 135 (6-7): : 816 - 843
12345