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1 results

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

  • Part of
  • Qun Chen
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 68 / Issue 2 / April 2000
    Published online by Cambridge University Press:
    09 April 2009, pp. 145-154
    Print publication:
    April 2000
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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.