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Multiple valued functions and integral currents
Camillo De Lellis and Emanuele SpadaroAbstract
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.
- Received:
- 05.06.13
- Published:
- 17.06.13