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.

Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps / J. Hirsch, S. Stuvard, D. Valtorta. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 371:6(2019), pp. 4303-4352.

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

S. Stuvard
;
2019

Abstract

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.
Q-valued functions; harmonic maps; singular set; rectifiability; Reifenberg theorem; quantitative stratification
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850244
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