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

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.

To appear at Proceedings of the American Mathematical Society

References in corpus (5)

• On the subRiemannian cut locus in a model of free two-step Carnot group
• Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries
• Curvature exponent and geodesic dimension on Sard-regular Carnot groups
• Curvature exponent of sub-Finsler Heisenberg groups
• SubRiemannian cut time and cut locus in Reiter-Heisenberg groups