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arXiv · 1409.2320

Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result

Matteo Focardi·Andrea Marchese·Emanuele Spadaro
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Abstract

In this note we prove an abstract version of a recent quantitative stratifcation priciple introduced by Cheeger and Naber (Invent. Math., 191 (2013), no. 2, 321-339; Comm. Pure Appl. Math., 66 (2013), no. 6, 965-990). Using this general regularity result paired with an $\varepsilon$-regularity theorem we provide a new estimate of the Minkowski dimension of the set of higher multiplicity points of a Dir-minimizing Q-valued function. The abstract priciple is applicable to several other problems: we recover recent results in the literature and we obtain also some improvements in more classical contexts.

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Matteo Focardi, Andrea Marchese, Emanuele Spadaro. 2014-09-08. Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result. https://arxiv.org/abs/1409.2320

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