4 problems

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Failure of the measure contraction property with strong Goh–Legendre geodesics
Failure of the measure contraction property with strong Goh–Legendre geodesics. If there is a strong-Goh–Legendre geodesic $\gamma$ , then $\mathsf{d}^2:M\times M\to\mathbb{R}_+$ fa…
Conjectureopenmeasure-contraction-property optimal-transport sub-riemannian-geometryarXiv posted 2 days ago
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The nonintegral curvature exponent conjecture for step-two Carnot groups
Let $N_{\mathrm{CE}}$ denote the curvature exponent of a step-two Carnot group, namely the least $N$ for which the measure contraction property $\mathrm{MCP}(0,N)$ holds. Nonintegr…
Conjectureopencarnot-groups measure-contraction-property sub-riemannian-geometryarXiv posted 2 days ago
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The curvature exponent–lower-bound conjecture for Carnot groups
Let $N_{\mathrm{CE}}$ be the curvature exponent of a Carnot group, namely the least $N$ for which the measure contraction property $\mathrm{MCP}(0,N)$ holds. Let $N_0$ be the lower…
Conjectureopencarnot-groups measure-contraction-property sub-riemannian-geometryarXiv posted 2 days ago
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Rifford's curvature exponent–geodesic dimension conjecture for Carnot groups
Let $N_{\mathrm{CE}}$ be the curvature exponent of a Carnot group, namely the least $N$ for which the measure contraction property $\mathrm{MCP}(0,N)$ holds. Let $N_{\mathrm{GEO}}$ …
Conjectureopencarnot-groups measure-contraction-property sub-riemannian-geometryarXiv posted 2 days ago

4 problems

Failure of the measure contraction property with strong Goh–Legendre geodesics

The nonintegral curvature exponent conjecture for step-two Carnot groups

The curvature exponent–lower-bound conjecture for Carnot groups

Rifford's curvature exponent–geodesic dimension conjecture for Carnot groups