Resumen de Multiple valued functions and integral currents

Camillo de Lellis, Emanuele Nunzio Spadaro

• 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 [5–7].