Calculus of Variations and Geometric Measure Theory
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S. Stuvard

Multiple valued sections of vector bundles: the reparametrization theorem for $Q$-valued functions revisited

created by stuvard on 27 Apr 2017
modified on 08 Aug 2017



Inserted: 27 apr 2017
Last Updated: 8 aug 2017

Year: 2017

ArXiv: 1705.00054 PDF


We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's $Q$-valued functions. We study some relevant properties of such $Q$-multisections and apply the theory to provide an elementary and purely geometric proof of a delicate reparametrization theorem for multi-valued graphs which plays an important role in the regularity theory for higher codimension area minimizing currents \`a la Almgren-De Lellis-Spadaro.

Keywords: Almgren's $Q$-valued functions; integral currents; integral flat chains


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