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.

Multiple valued functions and integral currents / DE LELLIS, Camillo; Spadaro, EMANUELE NUNZIO. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 14:4(2015), pp. 1239-1269. [10.2422/2036-2145.201306_002]

Multiple valued functions and integral currents

Camillo De Lellis;Emanuele Spadaro.
2015

Abstract

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.
2015
rectifiable currents; multiple valued maps
01 Pubblicazione su rivista::01a Articolo in rivista
Multiple valued functions and integral currents / DE LELLIS, Camillo; Spadaro, EMANUELE NUNZIO. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 14:4(2015), pp. 1239-1269. [10.2422/2036-2145.201306_002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1117515
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