Commentarii Mathematici Helvetici


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Volume 93, Issue 4, 2018, pp. 737–779
DOI: 10.4171/CMH/449

Published online: 2018-11-20

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

Camillo De Lellis[1], Andrea Marchese[2], Emanuele Spadaro[3] and Daniele Valtorta[4]

(1) Universität Zürich, Switzerland
(2) Universität Zürich, Switzerland
(3) Universität Leipzig, Germany
(4) Universität Zürich, Switzerland

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: Multiple-valued functions, Dirichlet energy, rectifiability, singularities, regularity

De Lellis Camillo, Marchese Andrea, Spadaro Emanuele, Valtorta Daniele: Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps. Comment. Math. Helv. 93 (2018), 737-779. doi: 10.4171/CMH/449