Mathematische Zeitschrift

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

Energy concentration for almost harmonic maps and the Willmore functional

Article

Abstract

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.

Keywords

Riemannian Manifold Energy Concentration Open Domain Compact Riemannian Manifold Tension Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Courant InstituteNew YorkUSA

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