Curvature exponent and geodesic dimension on Sard-regular Carnot groups

Abstract

In this paper we characterize the geodesic dimension $N_{GEO}$ and give a new lower bound to the curvature exponent $N_{CE}$ on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which $N_{CE}>N_{GEO}$: this answers a question posed by Rizzi in arXiv:1510.05960v4 [math.MG].

References in corpus (7)

• Curvature: a variational approach
• Sard Property for the endpoint map on some Carnot groups
• Sharp measure contraction property for generalized H-type Carnot groups
• Sub-Riemannian interpolation inequalities
• Measure contraction properties of Carnot groups
• Spectral multipliers on $2$-step groups: topological versus homogeneous dimension
• Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres

Cited by in corpus (2)

• On gradient estimates of the heat semigroups on step-two Carnot groups
• On the lower bound of the curvature exponent on step-two Carnot groups