Decay estimates for Rivi\`ere's equation, with applications to   regularity and compactness
  We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in $\mathbb{R}^2$ introduced by Rivi\`ere. Applications include sharp regularity results and compactness theorems which generalise a large amount of previous geometric PDE theory, including some of the theory of harmonic and almost-harmonic maps from surfaces. 
Ben Sharp and Peter Topping
math.AP math.DG