JournalszaaVol. 21, No. 3pp. 561–568

On Topological Singular Set of Maps with Finite 3-Energy into S3S^3

  • M.R. Pakzad

    CMLA-ENS, Cachan, France
On Topological Singular Set of Maps with Finite 3-Energy into $S^3$ cover
Download PDF

Abstract

We prove that the topological singular set of a map in W1,3(M,S3)W^{1,3} (M, \mathbb S^3) is the boundary of an integer-multiplicity rectifiable current in MM, where MM is a closed smooth manifold of dimension greater than 3 and S3\mathbb S^3 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 W1,3(M,S3)W^{1,3} (M, \mathbb S^3).

Cite this article

M.R. Pakzad, On Topological Singular Set of Maps with Finite 3-Energy into S3S^3. Z. Anal. Anwend. 21 (2002), no. 3, pp. 561–568

DOI 10.4171/ZAA/1094