Energy concentration for almost harmonic maps and the Willmore functional

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 ui: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.