  The present paper investigates the sub-Riemannian version of the equivalence
between the curvature-dimension conditions and strong Brunn-Minkowski
inequalities in the sub-Riemannian Heisenberg group Hn. We adopt the optimal
transport and approximation of Hn developed by Ambrosio and Rigot [1] and
combine the celebrated works by M. Magnabosco, L. Portinale and T. Rossi [17]
to confirm this.
