Global estimates and energy identities for elliptic systems with   antisymmetric potentials
  We derive global estimates in critical scale invariant norms for solutions of elliptic systems with antisymmetric potentials and almost holomorphic Hopf differential in two dimensions. Moreover we obtain new energy identities in such norms for sequences of solutions of these systems. The results apply to harmonic maps into general target manifolds and surfaces with prescribed mean curvature. In particular our results confirm a conjecture of Rivi\`ere in the two-dimensional setting. 
Tobias Lamm and Ben Sharp
math.AP math.DG