Multiple valued functions and integral currents

• Camillo De Lellis ^[1] ; Emanuele Spadaro ^[2]
  1. [1] University of Zurich

     University of Zurich

     Zürich, Suiza

     
  2. [2] Max-Planck-Institut für Mathemtik in den Naturwissenschaften, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 4, 2015, págs. 1239-1269
• Idioma: inglés
• Enlaces
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• Resumen

  • 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].