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math.DG2025
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…
math.DG2025
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…