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2008, Volume 3, Issue 1: 85-95. Doi: 10.3934/nhm.2008.3.85

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Leaf superposition property for integer rectifiable currents

1.
Scuola Normale Superiore, p.za dei Cavalieri 7, Pisa, I-56126
2.
Dipartimento di Matematica, Università degli Studi di Parma, viale G.P. Usberti 53/A (Campus), 43100 Parma
3.
Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris

Received: June 2007

Revised: September 2007

Published: March 2008

Abstract / Introduction Related Papers Cited by

Abstract

We consider the class of integer rectifiable currents without boundary in $\R^n\times\R$ satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

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Mathematics Subject Classification: Primary: 49Q15; Secondary: 26B30, 30C55.

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