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.
Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups
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abstract
We prove that two-step analytic sub-Riemannian structures on a compact analytic manifold equipped with a smooth measure and Lipschitz Carnot groups satisfy measure contraction properties.
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2019 1verdicts
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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.