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

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sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's $Q$-valued functions.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

V2 is the final version, to appear in Comm. Anal. Geom

References in corpus (6)

• Q-valued functions revisited
• Collapsing and the convex hull property in a soap film capillarity model
• Smoothness of collapsed regions in a capillarity model for soap films
• Plateau's problem as a singular limit of capillarity problems
• Fine structure of the singular set of area minimizing hypersurfaces modulo $p$
• An Allard-type boundary regularity theorem for $2d$ minimizing currents at smooth curves with arbitrary multiplicity

Cited by in corpus (1)

• Area minimizing currents mod $2Q$: linear regularity theory