Regularity properties of nonlocal minimal surfaces via limiting   arguments
  We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter $s$ when $s\rightarrow 1^-$.   As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the nonlocal minimal surfaces are smooth when the dimension of the ambient space is less or equal than 7 and $s$ is close to 1. 
Luis Caffarelli and Enrico Valdinoci
math.AP