Density estimates and the fractional Sobolev inequality for sets of zero s-mean curvature

We prove that measurable sets E Rⁿ with locally finite perimeter and zero s-mean curvature satisfy the surface density estimates: align* Per (E; BR (x) ) CR^n-1 align* for all R>0, x ^ E. The C depends only on n and s, and remains bounded as s 1^-. As an application, we prove that the fractional Sobolev inequality holds on the boundary of sets with zero s-mean curvature.