The Calabi-Yau equation on the Kodaira-Thurston manifold, viewed as an   S^1-bundle over a 3-torus
  We prove that the Calabi-Yau equation on the Kodaira-Thurston manifold has a unique solution for every $S^1$-invariant initial datum. 
Ernesto Buzano, Anna Fino, Luigi Vezzoni
math.DG