3D crystal: how flat its flat facets are?
  We investigate the hypothesis that the (random) crystal of the $(-)$-phase inside the $(+)$-phase of the 3D canonical Ising model has flat facets. We argue that it might need to be weakened, due to the possibility of formation of extra monolayer on a facet. We then prove this weaker hypothesis for the Solid-On-Solid model. 
Thierry Bodineau, Roberto H. Schonmann, Senya Shlosman