Abstract
AbstractLet 𝒴 be a smooth, compact, oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps uk:Bn → 𝒴 with an equibounded Dirichlet integral give rise to elements of the space cart2,1 (Bn × 𝒴). Assume that 𝒴 is 1‐connected and that its 2‐homology group has no torsion. In any dimension n we prove that every element T in cart2,1 (Bn × 𝒴) with no singular vertical part can be approximated weakly in the sense of currents by a sequence of graphs of smooth maps uk:Bn → 𝒴 with Dirichlet energies converging to the energy of T. © 2006 Wiley Periodicals, Inc.
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