Inserted: 27 apr 2017
Last Updated: 8 aug 2017
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valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's $Q$-valued functions.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