  The de Giorgi theory for minimal surfaces consists in studying sets whose
indicator function is a (local) minimum of the BV norm. In this paper we
replace the BV norm by the $H^\sigma$ norm, with $\sigma<1/2$, and try to
understand what the minimisers look like. Parallel to the de Giorgi theory we
prove that, if the boundary of a minimiser is sufficiently flat in the unit
ball, then it is a smooth piece of hypersurface.
