We prove that the topological singular set of a map in is the boundary of an integer-multiplicity rectifiable current in , where is a closed smooth manifold of dimension greater than 3 and is the three-dimensional sphere. Also, we prove that the mass of the minimal integer-multiplicity rectifiable current taking this set as the boundary is a strongly continuous functional on .
Cite this article
M.R. Pakzad, On Topological Singular Set of Maps with Finite 3-Energy into . Z. Anal. Anwend. 21 (2002), no. 3, pp. 561–568DOI 10.4171/ZAA/1094