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sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note `` extit{Some useful techniques for dealing with multiple valued functions}'' and generalizes Almgren's $Q$-valued functions.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

S. Stuvard
2020-04-04

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valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note `` extit{Some useful techniques for dealing with multiple valued functions}'' and generalizes Almgren's $Q$-valued functions.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.
Almgren's Q-valued functions; Integral currents; Reparametrization
Settore MAT/05 - Analisi Matematica
https://arxiv.org/abs/1705.00054
File in questo prodotto:
File Dimensione Formato  
1705.00054.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 423.78 kB
Formato Adobe PDF
423.78 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850465
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact