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

  • Camillo De Lellis

    Universität Zürich, Switzerland
  • Andrea Marchese

    Universität Zürich, Switzerland
  • Emanuele Spadaro

    Universität Leipzig, Germany
  • Daniele Valtorta

    Universität Zürich, Switzerland

Abstract

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

Cite this article

Camillo De Lellis, Andrea Marchese, Emanuele Spadaro, Daniele Valtorta, Rectifiability and upper Minkowski bounds for singularities of harmonic -valued maps. Comment. Math. Helv. 93 (2018), no. 4, pp. 737–779

DOI 10.4171/CMH/449