Calculus of Variations and Geometric Measure Theory

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 01 Dec 2020


Published Paper

Inserted: 6 dec 2016
Last Updated: 1 dec 2020

Journal: Comm. Math. Helv.
Volume: 93
Number: 4
Pages: 737-779
Year: 2018


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