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arXiv · 1708.02116

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

Jonas Hirsch·Salvatore Stuvard·Daniele Valtorta
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Abstract

In this paper we study the singular set of Dirichlet-minimizing $Q$-valued maps from $\mathbb{R}^m$ into a smooth compact manifold $\mathcal{N}$ 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 $\mathcal{N}$ being non-positively curved but not simply connected does not imply continuity of the map.

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Jonas Hirsch, Salvatore Stuvard, Daniele Valtorta. 2017-08-07. Rectifiability of the singular set of multiple valued energy minimizing harmonic maps. https://doi.org/10.1090/tran/7595

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