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Volume of small balls and sub-Riemannian curvature in 3D contact manifolds
Journal of Symplectic Geometry  (IF0.707),  Pub Date : 2020-01-01, DOI: 10.4310/jsg.2020.v18.n2.a1
Davide Barilari, Ivan Beschastnyi, Antonio Lerario

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