Calculus of Variations and Geometric Measure Theory
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C. De Lellis - E. Spadaro

Multiple valued functions and integral currents

created by delellis on 02 Jul 2013
modified on 24 May 2017


Published Paper

Inserted: 2 jul 2013
Last Updated: 24 may 2017

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


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 [1,2,3].


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