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March  2008, 3(1): 85-95. doi: 10.3934/nhm.2008.3.85

Leaf superposition property for integer rectifiable currents

Luigi Ambrosio 1, , Gianluca Crippa 2, and  Philippe G. Lefloch 3,

1. 

Scuola Normale Superiore, p.za dei Cavalieri 7, Pisa, I-56126, Italy
2. 

Dipartimento di Matematica, Università degli Studi di Parma, viale G.P. Usberti 53/A (Campus), 43100 Parma, Italy
3. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France

Received  June 2007 Revised  September 2007 Published  January 2008

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.
Keywords: Metric spaces valued $BV$ functions, Multi-valued functions., Integer rectifiable currents, Currents in metric spaces, Cartesian currents.
Mathematics Subject Classification: Primary: 49Q15; Secondary: 26B30, 30C5.
Citation: Luigi Ambrosio, Gianluca Crippa, Philippe G. Lefloch. Leaf superposition property for integer rectifiable currents. Networks & Heterogeneous Media, 2008, 3 (1) : 85-95. doi: 10.3934/nhm.2008.3.85
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