Geodesic
Hermitian Harmonic Maps into Convex Balls
Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 113-122

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is a compact Hermitian manifold with non-empty boundary.
DOI : 10.4153/CMB-2007-011-1
Mots-clés : 58E15, 53C07, Hermitian harmonic map, Hermitian manifold, convex ball 
Li, Zhen Yang; Zhang, Xi. Hermitian Harmonic Maps into Convex Balls. Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 113-122. doi: 10.4153/CMB-2007-011-1
@article{10_4153_CMB_2007_011_1,
     author = {Li, Zhen Yang and Zhang, Xi},
     title = {Hermitian {Harmonic} {Maps} into {Convex} {Balls}},
     journal = {Canadian mathematical bulletin},
     pages = {113--122},
     year = {2007},
     volume = {50},
     number = {1},
     doi = {10.4153/CMB-2007-011-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-011-1/}
}
TY  - JOUR
AU  - Li, Zhen Yang
AU  - Zhang, Xi
TI  - Hermitian Harmonic Maps into Convex Balls
JO  - Canadian mathematical bulletin
PY  - 2007
SP  - 113
EP  - 122
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-011-1/
DO  - 10.4153/CMB-2007-011-1
ID  - 10_4153_CMB_2007_011_1
ER  - 
%0 Journal Article
%A Li, Zhen Yang
%A Zhang, Xi
%T Hermitian Harmonic Maps into Convex Balls
%J Canadian mathematical bulletin
%D 2007
%P 113-122
%V 50
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-011-1/
%R 10.4153/CMB-2007-011-1
%F 10_4153_CMB_2007_011_1

[1] [1] Chen, J. Y., A boundary value problem for Hermitian harmonic maps and applications. Proc. Amer. Math. Soc. 124(1996), no. 9, 2853–2862. Google Scholar

[2] [2] Grunau, H. C. and Kühnel, M., On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemaniann manifolds. Math. Z. 249(2005), no. 2, 297–327. Google Scholar

[3] [3] Jäger, W. and Kaul, H., Uniqueness and stability of harmonic maps and their Jacobi fields. Manuscripta Math. 28(1979), no. 1–3, 269–291. Google Scholar

[4] [4] Jost, J., Harmonic Mappings Between Riemannian Manifolds. Proceedings of the Centre for Mathematic Analysis 4, Australian National University, Canberra, 1984. Google Scholar

[5] [5] Jost, J. and Yau, S. T., A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry. Acta Math. 170(1993), 221–254. Google Scholar

[6] [6] Ni, L., Hermitian harmonic maps from complete Hermitian manifolds to complete Riemannian manifolds. Math. Z. 232(1999), no. 2, 331–355. Google Scholar

[7] [7] Taylor, M. E., Partial Differential Equations. I. Basic Theory. Applied Mathematical Sciences 115, Springer-Verlag, New York, 1996. Google Scholar

Cité par Sources :