2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115500Let S be a C^2 H-minimal noncharacteristic hypersurface in the first Heisenberg group. We show that if S contains a graphical strip, then it is not a stable minimal surface. Moreover, we show that if S is a C^2 H-minimal noncharacteristic entire graph which is not itself a vertical plane, then S contains a graphical strip. Thus, as a corollary, we obtain an analogue of the Bernstein theorem: the only stable C^2 H-minimal noncharacteristic entire graphs are the vertical planes.33 pagesDifferential GeometryAnalysis of PDEstext