We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter s when s →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. © 2013 Elsevier Inc.
Caffarelli, L., & Valdinoci, E. (2013). Regularity properties of nonlocal minimal surfaces via limiting arguments. Advances in Mathematics, 248, 843–871. https://doi.org/10.1016/j.aim.2013.08.007