Minimizing 1/2-harmonic maps into spheres

@article{Millot2019Minimizing1M,
  title={Minimizing 1/2-harmonic maps into spheres},
  author={Vincent Millot and Marc Pegon},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2019},
  volume={59},
  pages={1-37}
}
  • V. Millot, Marc Pegon
  • Published 2019
  • Mathematics, Physics
  • Calculus of Variations and Partial Differential Equations
In this article, we improve the partial regularity theory for minimizing 1/2-harmonic maps of Millot and Sire (Arch Ration Mech Anal 215:125–210, 2015), Moser( J Geom Anal 21:588–598, 2011) in the case where the target manifold is the $$(m-1)$$ ( m - 1 ) -dimensional sphere. For $$m\geqslant 3$$ m ⩾ 3 , we show that minimizing 1/2-harmonic maps are smooth in dimension 2, and have a singular set of codimension at least 3 in higher dimensions. For $$m=2$$ m = 2 , we prove that, up to an… Expand
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