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In this paper we study global Poincare inequalities on balls in a large classof sub-Riemannian manifolds satisfying the generalized curvature dimensioninequality introduced by F.Baudoin and N.Garofalo. As a corollary, we prove theuniqueness of solutions for the subelliptic heat equation. Our results apply inparticular to CR Sasakian manifolds with Tanaka-Webster-Ricci curvature boundedfrom below and Carnot groups of step two.

Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators