Calculus of Variations and Geometric Measure Theory

C. De Lellis - E. Spadaro

Multiple valued functions and integral currents

created by delellis on 02 Jul 2013
modified on 27 Jun 2019


Published Paper

Inserted: 2 jul 2013
Last Updated: 27 jun 2019

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Volume: 14
Pages: 1239–1269
Year: 2015

ArXiv: 1306.1188 PDF


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.