Existence and Liouville theorems for V-harmonic maps from complete manifolds

被引：42

作者：

Chen, Qun ^{[2
,3
]}

Jost, Juergen ^{[1
,2
]}

Qiu, Hongbing ^{[3
]}

机构：

[1] Univ Leipzig, Dept Math, D-04091 Leipzig, Germany

[2] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2012年 / 42卷 / 04期

基金：

欧洲研究理事会;

关键词：

V-Harmonic map; Noncompact manifold; Existence; Liouville theorem; V-Laplacian comparison theorem; COMPLETE RIEMANNIAN-MANIFOLDS; EMERY-RICCI TENSOR; FINSLER MANIFOLDS; HEAT FLOWS; GEOMETRY;

D O I：

10.1007/s10455-012-9327-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish existence and uniqueness theorems for V-harmonic maps from complete noncompact manifolds. This class of maps includes Hermitian harmonic maps, Weyl harmonic maps, affine harmonic maps, and Finsler harmonic maps from a Finsler manifold into a Riemannian manifold. We also obtain a Liouville type theorem for V-harmonic maps. In addition, we prove a V-Laplacian comparison theorem under the Bakry-Emery Ricci condition.

引用

页码：565 / 584

页数：20

共 38 条

[1]

[Anonymous], 1983, ELLIPTIC PARTIAL DIF

[2]

Cao H.D., 2010, RECENT ADV GEOMETRIC, V11, P1

[3] Finsler Laplacians and minimal-energy maps [J].

Centore, P .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2000, 11 (01) :1-13

[4]

Chen Qun, 2011, PREPRINT

[5]

Cheng S. Y., 1980, Proc. Symp. Pure Math, V36, P147

[6] ON THE LIOUVILLE THEOREM FOR HARMONIC MAPS [J].

CHOI, HI .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 85 (01) :91-94

[7] Generic mean curvature flow I; generic singularities [J].

Colding, Tobias H. ;

Minicozzi, William P., II .

ANNALS OF MATHEMATICS, 2012, 175 (02) :755-833

[8]

Ding Q., 2011, ARXIV11011411V1

[9]

Ding W. Y., 1991, INT J MATH, V2, P617

[10]

Dong T., 2010, NONLINEAR ANAL, V72, P3457

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