# Volume of small balls and sub-Riemannian curvature in 3D contact manifolds

arXiv: https://arxiv.org/abs/1802.10155 · HTML: https://mlsanity.com/paper/1802.10155/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2018.

## Built on by (most cited first, 1 of 1)

- [Representation Gap: Explaining the Unreasonable Effectiveness of Neural Networks from a Geometric Perspective](https://mlsanity.com/paper/2605.21692/) (2026)

## Abstract (arXiv)

We compute the asymptotic expansion of the volume of small sub-Riemannian balls in a contact 3-dimensional manifold, and we express the first meaningful geometric coefficients in terms of geometric invariants of the sub-Riemannian structure