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The Lott-Sturm-Villani curvature-dimension condition $\mathsf{CD}(K,N)$provides a synthetic notion for a metric-measure space to have curvaturebounded from below by $K$ and dimension bounded from above by $N$. It wasproved by Juillet that a large class of \sr manifolds do not satisfy the$\mathsf{CD}(K,N)$ condition, for any $K\in\mathbb R$ and $N\in(1,\infty)$.However, his result does not cover the case of almost-Riemannian manifolds. Inthis paper, we address the problem of disproving the $\mathsf{CD}$ condition inthis setting, providing a new strategy which allows us to contradict the$1$-dimensional version of the $\mathsf{CD}$ condition. In particular, we provethat $2$-dimensional almost-Riemannian manifolds and strongly regularalmost-Riemannian manifolds do not satisfy the $\mathsf{CD}(K,N)$ condition forany $K\in\mathbb R$ and $N\in(1,\infty)$.

Almost-Riemannian manifolds do not satisfy the $\mathsf{CD}$ condition