On Topological Singular Set of Maps with Finite 3-Energy into $S^3$
On Topological Singular Set of Maps with Finite 3-Energy into $S^3$
We prove that the topological singular set of a map in W^{1,3} (M, \mathbb S^3) is the boundary of an integer-multiplicity rectifiable current in M , where M is a closed smooth manifold of dimension greater than 3 and \mathbb S^3 is the three-dimensional sphere. Also, we prove that the …