MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Multiple valued functions and integral currents

Camillo De Lellis and Emanuele 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.

Jun 5, 2013
Jun 17, 2013

Related publications

2015 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Multiple valued functions and integral currents

In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 14 (2015) 4, pp. 1239-1269