Harmonic maps with potential

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Abstract

Let (M,g) and (N,h) be two Riemannian manifolds, and G : N → ℝ a given function. If f : M → N is a smooth map, we set E G(f)=1/2 ∫ M [|df|2 − 2G(f)]dv g. We establish some variational properties and some existence results for the functional E G(f): in particular, we analyse the case of maps into a sphere.

Mathematics Subject Classification

58E20 49A10 35J20 

Key words

Harmonic maps the Landau-Lifshitz equation the Neumann motion 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BrestBrest CedexFrance
  2. 2.Dipartimento di MatematicaUnicalArcavata di Rende (CS)Italy

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