  We prove that measurable sets $E\subset \mathbb R^n$ with locally finite
perimeter and zero $s$-mean curvature satisfy the surface density estimates:
\begin{align*}
  \operatorname{Per} (E; B_R(x)) \geq CR^{n-1} \end{align*} for all $R>0$,
$x\in \partial^\ast E$. The $C$ depends only on $n$ and $s$, and remains
bounded as $s\to 1^-$. As an application, we prove that the fractional Sobolev
inequality holds on the boundary of sets with zero $s$-mean curvature.
