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sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note  extit{Some useful techniques for dealing with multiple valued functions}'' and generalizes Almgren's $Q$-valued functions.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

Multiple valued sections of vector bundles: the reparametrization theorem for Q-valued functions revisited / S. Stuvard. - (2020 Apr 04).

### 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valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note  extit{Some useful techniques for dealing with multiple valued functions}'' and generalizes Almgren's $Q$-valued functions.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.
##### Scheda breve Scheda completa Scheda completa (DC)
Almgren's Q-valued functions; Integral currents; Reparametrization
Settore MAT/05 - Analisi Matematica
https://arxiv.org/abs/1705.00054
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850465