A quasi-convex relaxation of the curvature-dimension condition gives dimension-independent Poincaré and log-Sobolev constants on Heisenberg groups and other sub-Riemannian manifolds, up to a universal factor.
Comparison theorems on H-type sub-Riemannian manifolds
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abstract
On H-type sub-Riemannian manifolds we establish sub-Hessian and sub-Laplacian comparison theorems which are uniform for a family of approximating Riemannian metrics converging to the sub-Riemannian one. We also prove a sharp sub-Riemannian Bonnet-Myers theorem that extends to this general setting results previously proved on contact and quaternionic contact manifolds.
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The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds
A quasi-convex relaxation of the curvature-dimension condition gives dimension-independent Poincaré and log-Sobolev constants on Heisenberg groups and other sub-Riemannian manifolds, up to a universal factor.