Density results relative to the Dirichlet energy of mappings into a manifold


Let Y be a smooth compact oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps uk : B n → Y with equibounded Dirichlet integral give rise to elements of the space cart(B × 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 cart(B ×Y) with no… (More)