2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74977In 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 $\hhn$.16 pages, 1 figureDifferential GeometryMetric GeometryPrimary 53C17, Secondary 49Q20text