Unique Ergodicity of Harmonic Currents on Singular Foliations of P2
  Let F be a holomorphic foliation of P^2 by Riemann surfaces. Assume all the singular points of F are hyperbolic. If F has no algebraic leaf, then there is a unique positive harmonic $(1,1)$ current $T$ of mass one, directed by F. This implies strong ergodic properties for the foliation. We also study the harmonic flow associated to the current $T.$ 
John Erik Fornaess, Nessim Sibony