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

Mohammad Reza Pakzad | Zendy

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

Author(s) -

Mohammad Reza Pakzad

Publication year - 2002

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1094

Subject(s) - set (abstract data type) , topology (electrical circuits) , mathematics , energy (signal processing) , pure mathematics , computer science , combinatorics , programming language , statistics

We prove that the topological singular set of a map in W (M,S) is the boundary of an integer-multiplicity rectifiable current in M , where M is a closed smooth manifold of dimension greater than 3 and S 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 (M,S).

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