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

Equivalence of Strong Brunn-Minkowski Inequalities and CD Conditions in Heisenberg Groups