66 citations · 67 across the 5 of their papers we have counts for
6 papers · 1 filter
Curvature measures and the sub-Riemannian Gauss-Bonnet theorem
Davide Barilari, Eugenio Bellini, Andrea Pinamonti
We adopt a measure-theoretic perspective on the Riemannian approximation scheme proving a sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds. We show that the…
Magnetic flows on 3D contact sub-Riemannian manifolds via the Rumin complex
Davide Barilari, Tania Bossio, Valentina Franceschi
We show that the appropriate notion of magnetic field on three-dimensional contact sub-Riemannian manifolds is given by a closed Rumin differential two-form. We introduce horizonta…
Bakry-Émery curvature and model spaces in sub-Riemannian geometry
Davide Barilari, Luca Rizzi
We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparis…
Volume of small balls and sub-Riemannian curvature in 3D contact manifolds
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 t…
Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions
Davide Barilari, Ugo Boscain, Enrico Le Donne +1
In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated w…
A formula for Popp's volume in sub-Riemannian geometry
Davide Barilari, Luca Rizzi
For an equiregular sub-Riemannian manifold M, Popp's volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization…