Mathematische Zeitschrift

, Volume 251, Issue 2, pp 293–311 | Cite as

Energy concentration for almost harmonic maps and the Willmore functional



Let Ω be an open domain in ℝ3 or ℝ4 and N a smooth, compact Riemannian manifold. We consider the Dirichlet energy E(u) for maps u:Ω→N and its negative L2-gradient, the tension field τ(u). We study sequences of maps u i :Ω→N with Open image in new window If the maps are sufficiently regular, we find strong H1-subconvergence away from a generalized submanifold in Ω. If the limit map is regular, too, we can estimate a Willmore-type energy of this generalized submanifold.


Riemannian Manifold Energy Concentration Open Domain Compact Riemannian Manifold Tension Field 
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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Courant InstituteNew YorkUSA

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