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Stability and constant boundary-value problems of harmonic maps with potential

Part of: Global differential geometry Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  09 April 2009

Qun Chen
Qun Chen
Affiliation:
Mathematics Department Central China Normal University Wushan 430079 China School of Mathematical Science Wuhan University Wuhan 430072 China e-mail: [email protected]
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Abstract

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Let M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.

Keywords

Harmonic mapspotentialstabilityboundary-value.

MSC classification

Secondary: 58E20: Harmonic maps , etc. 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 145 - 154
Copyright
Copyright © Australian Mathematical Society 2000

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