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

created by stuvard on 27 Apr 2017
modified on 09 Nov 2017

[BibTeX]

Submitted Paper

Inserted: 27 apr 2017
Last Updated: 9 nov 2017

Year: 2017

ArXiv: 1705.00054 PDF

Abstract:

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valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's $Q$-valued functions.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.