MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.


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