JournalscmhVol. 93, No. 4pp. 737–779

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

  • Camillo De Lellis

    Universität Zürich, Switzerland

  • Andrea Marchese

    Universität Zürich, Switzerland

  • Emanuele Spadaro

    Universität Leipzig, Germany

  • Daniele Valtorta

    Universität Zürich, Switzerland
Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps cover
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Abstract

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

Cite this article

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

DOI 10.4171/CMH/449