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arXiv · 1306.1188

Multiple valued functions and integral currents

Camillo De Lellis·Emanuele Spadaro
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Abstract

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.

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Camillo De Lellis, Emanuele Spadaro. 2013-06-05. Multiple valued functions and integral currents. https://arxiv.org/abs/1306.1188

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