On the lower bound of the curvature exponent on step-two Carnot groups

2025/04/28 by Zhang, Ye
#53C17 #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2504.20005

Abstract

In this work, we show that there exists a step-two Carnot group on which the new lower bound of the curvature exponent given in arXiv:2308.15811v2 can be strictly less than the curvature exponent by studying the convergence of the structure constants of Lie algebra.

Citations

• New properties of length-extremals in free step-2 rank-4 Carnot groups
• Curvature exponent of sub-Finsler Heisenberg groups
• Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups
• SubRiemannian cut time and cut locus in Reiter-Heisenberg groups
• Measure contraction property, curvature exponent and geodesic dimension of sub-Finsler ℓ^p-Heisenberg groups
• Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries
• On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups
• Ricci curvatures in Carnot groups
• On 2-step, corank 2 nilpotent sub-Riemannian metrics
• Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries

Related

• On gradient estimates of the heat semigroups on step-two Carnot groups
• New properties of length-extremals in free step-2 rank-4 Carnot groups
• Ricci curvatures in Carnot groups
• Asymptotics of Riemannian Lie groups with nilpotency step 2
• Curvature exponent of sub-Finsler Heisenberg groups