On topological singular set of maps with finite 3-energy into \(S^3\) (Q1848653)

Summary: The author proves 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, he proves that the mass of the minimal integer-multiplicity rectifiable current taking this set as the boundary is a strongly continuous functional on \(W^{1,3}(M,\mathbb{S}^3)\).