Liouville-type theorems for biharmonic maps between Riemannian manifolds

被引:36
作者
Baird, Paul [1 ]
Fardoun, Ali [1 ]
Ouakkas, Seddik
机构
[1] Univ Bretagne Occidentale, Lab CNRS, UMR 6205, Dept Math, F-29238 Brest 3, France
关键词
Liouville theorem; biharmonic map; HARMONIC MAPS;
D O I
10.1515/ACV.2010.003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove Liouville type theorems for biharmonic maps from complete manifolds and from Euclidean balls.
引用
收藏
页码:49 / 68
页数:20
相关论文
共 50 条
[31]   Equivariant biharmonic maps between manifolds with metrics of signature [J].
Chiang Y.-J. .
Journal of Geometry, 2018, 109 (1)
[32]   Biharmonic curves along Riemannian maps [J].
Karakas, Gizem Koprulu ;
Sahin, Bayram .
FILOMAT, 2024, 38 (01) :227-239
[33]   Harmonic maps and biharmonic Riemannian submersions [J].
Urakawa, Hajime .
NOTE DI MATEMATICA, 2019, 39 (01) :1-23
[34]   Complement of gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds [J].
Wang, Wen .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (06) :2078-2083
[35]   Existence and Liouville theorems for V-harmonic maps from complete manifolds [J].
Chen, Qun ;
Jost, Juergen ;
Qiu, Hongbing .
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2012, 42 (04) :565-584
[36]   A Bayesian Approach to the Estimation of Maps between Riemannian Manifolds [J].
Butler, L. T. ;
Levit, B. .
MATHEMATICAL METHODS OF STATISTICS, 2007, 16 (04) :281-297
[37]   A structure theorem for polyharmonic maps between Riemannian manifolds [J].
Branding, Volker .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 273 :14-39
[38]   Hamilton's gradient estimates and Liouville theorems for porous medium equations on noncompact Riemannian manifolds [J].
Zhu, Xiaobao .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 402 (01) :201-206
[39]   Biharmonic maps into a Riemannian manifold of non-positive curvature [J].
Nakauchi, Nobumitsu ;
Urakawa, Hajime ;
Gudmundsson, Sigmundur .
GEOMETRIAE DEDICATA, 2014, 169 (01) :263-272
[40]   Conformal Change of Riemannian Metrics and Biharmonic Maps [J].
Naito, Hisashi ;
Urakawa, Hajime .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2014, 63 (06) :1631-1657