An Exactly Solved Model of Three Dimensional Surface Growth in the   Anisotropic KPZ Regime
  We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions. 
M. Praehofer, H. Spohn