Multiple valued functions and integral currents
Camillo De Lellis and Emanuele Spadaro
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Submission date: 05. Jun. 2013
published in: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 14 (2015) 4, p. 1239-1269
DOI number (of the published article): 10.2422/2036-2145.201306_002
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We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current; we derive explicit formulae for the boundary, the mass and the first variations along certain specific vector-fields; and exploit this connection to derive a delicate reparametrization property for multiple valued functions. These results play a crucial role in our new proof of the partial regularity of area minimizing currents.