Calculus of Variations and Geometric Measure Theory
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C. De Lellis - A. Marchese - E. Spadaro - D. Valtorta

Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps

created by marchese on 06 Dec 2016
modified by delellis on 17 Jul 2018


Accepted Paper

Inserted: 6 dec 2016
Last Updated: 17 jul 2018

Journal: To appear in Comm. Math. Helv.
Pages: 32
Year: 2016


In this article we prove that the singular set of Dirichlet-minimizing $Q$-valued functions is countably $(m − 2)$-rectifiable and we give upper bounds for the $(m − 2)$-dimensional Minkowski content of the set of singular points with multiplicity $Q$.

Keywords: Rectifiability, regularity, Dirichlet energy, Multiple-valued functions, Singularities


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