Year: 2026
Type: article
Abstract: We prove that a sub-Riemannian manifold with a full-support Radon measure is never CD ( K , N ) \operatorname{CD}(K,N) for any K ∈ R K\in\mathbb{R} and N ∈ ( 1 , ∞ ) N\in(1,\infty) unless it is Riemannian. This generalizes previous non- CD \operatorname{CD} results for sub-Riemannian manifolds, where a measure with smooth and positive density is considered. Our proof is based on the analysis of the tangent cones and the geodesics within. Secondly, we construct new RCD \operatorname{RCD} structures on R n \mathbb{R}^{n} , named cone-Grushin spaces, that fail to be sub-Riemannian due to the lack of a scalar product along a curve, yet exhibit characteristic features of sub-Riemannian geometry, such as horizontal directions, large Hausdorff dimension, and inhomogeneous metric dilations.
Authors: Dimitri Navarro, Jiayin Pan
Institution: University of California, Santa Cruz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4416878741
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