A note on the diameter of small sub-Riemannian balls
Optimization and Control
2026-03-13 v2 Differential Geometry
Metric Geometry
Abstract
We observe that the diameter of small (in a locally uniform sense) balls in sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to , the diameter is arbitrarily close to twice the radius. Both results hold independently of the bracket-generating condition.
Keywords
Cite
@article{arxiv.2505.02790,
title = {A note on the diameter of small sub-Riemannian balls},
author = {Marco Di Marco and Gianluca Somma and Davide Vittone},
journal= {arXiv preprint arXiv:2505.02790},
year = {2026}
}
Comments
6 pages