Calculus of Variations and Geometric Measure Theory

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 24 Jul 2022


Published Paper

Inserted: 27 apr 2017
Last Updated: 24 jul 2022

Journal: Comm. Anal. Geom.
Volume: 30
Number: 1
Pages: 207-255
Year: 2022
Doi: 10.4310/CAG.2022.v30.n1.a4

ArXiv: 1705.00054 PDF
Links: CAG


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sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's $Q$-valued functions.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