Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps

In this paper we study the singular set of energy minimizing Q-valued maps from R-m into a smooth compact manifold N without boundary. Similarly to what happens in the case of single valued minimizing harmonic maps, we show that this set is always (m - 3)-rectifiable with uniform Minkowski bounds. Moreover, as opposed to the single-valued case, we prove that the target N being nonpositively curved but not simply connected does not imply continuity of the map.