In this paper we study the singular set of energy minimizing Q-valued maps from Rm 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.
Hirsch, J., Stuvard, S., Valtorta, D. (2019). Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 371(6), 4303-4352 [10.1090/tran/7595].
Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps
Valtorta, D
2019
Abstract
In this paper we study the singular set of energy minimizing Q-valued maps from Rm 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.
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