  In this paper we study sets in the $n$-dimensional Heisenberg group $\hhn$
which are critical points, under a volume constraint, of the sub-Riemannian
perimeter associated to the distribution of horizontal vector fields in $\hhn$.
We define a notion of mean curvature for hypersurfaces and we show that the
boundary of a stationary set is a constant mean curvature (CMC) hypersurface.
Our definition coincides with previous ones.
  Our main result describes which are the CMC hypersurfaces of revolution in
$\hhn$. The fact that such a hypersurface is invariant under a compact group of
rotations allows us to reduce the CMC partial differential equation to a system
of ordinary differential equations. The analysis of the solutions leads us to
establish a counterpart in the Heisenberg group of the Delaunay classification
of constant mean curvature hypersurfaces of revolution in the Euclidean space.
Hence we classify the rotationally invariant isoperimetric sets in $\hhn$.
