  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.
