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

De Lellis, Camillo; Marchese, Andrea; Spadaro, Emanuele; Valtorta, Daniele (2018). Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps. Commentarii Mathematici Helvetici (CMH), 93(4):737-779.

## Abstract

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 $Q$.

## Abstract

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 $Q$.

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