The Martinet and Engel sub-Riemannian structures do not satisfy the measure contraction property for any curvature bound K and dimension N, so MCP-type Ricci lower bounds are not universal beyond step two.
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Failure of the measure contraction property via quotients in higher-step sub-Riemannian structures
The Martinet and Engel sub-Riemannian structures do not satisfy the measure contraction property for any curvature bound K and dimension N, so MCP-type Ricci lower bounds are not universal beyond step two.