Abstract
Harmonic maps with potential from complete manifolds are considered. This is a new kind of maps more general than the usual harmonic maps relating to many interesting problems such as equilibrium system of ferromagnetic spin chain and Neumann motion. Aiming at the general properties, the author derives basic gradient estimates and then Liouville type results for these maps, which are interesting in constrast to those of the usual harmonic maps for the presence of potentials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fardoun, A., Ratto, A., Harmonic maps with potential,Calc. Var., 1997, 5: 183.
Li, J. Y., The heat flows and harmonic maps of complete noncompact Riemannian manifolds,Math. Z., 1993, 212: 161.
Avilhs, P., Choi, H., Micallef, M., Boundary behavior of harmonic maps on non-smooth domains and complete negatively curved manifolds,J. Funct. Anal., 1991, 99: 293.
Shen, Y., A Liouville theorem for harmonic maps,Amer. j. Math., 1995, 117: 773.
Xin, Y. L.,Geometry of Harmonic Maps, Boston-Basel-Berlin: Birkhauser, 1996.
Scheon, R., Yau, S. T., Harmonic maps and the topology of stable hypersurfaces and manifolds of non-negative Ricci curvature,Comm. Math. Helv., 1976, 51: 333.
Author information
Authors and Affiliations
About this article
Cite this article
Chen, Q. Harmonic maps with potential from complete manifolds. Chin. Sci. Bull. 43, 1780–1786 (1998). https://doi.org/10.1007/BF02883371
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02883371