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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 561–568
DOI: 10.4171/ZAA/1094

Published online: 2002-09-30

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

M.R. Pakzad[1]

(1) CMLA-ENS, Cachan, France

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

Keywords: Topological singularities, minimal connections, flat chains and rectifiable currents, Sobolev spaces between manifolds

Pakzad M.R.: On Topological Singular Set of Maps with Finite 3-Energy into $S^3$. Z. Anal. Anwend. 21 (2002), 561-568. doi: 10.4171/ZAA/1094