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valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note `` extit{Some useful techniques for dealing with multiple valued functions}'' and generalizes Almgren's $Q$-valued functions.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. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - 30:1(2022), pp. 207-255. [10.4310/CAG.2022.v30.n1.a4]
Multiple valued sections of vector bundles: the reparametrization theorem for Q-valued functions revisited
S. Stuvard
2022
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valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note `` extit{Some useful techniques for dealing with multiple valued functions}'' and generalizes Almgren's $Q$-valued functions.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.File | Dimensione | Formato | |
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