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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.SG2025
On the tightness of left-invariant contact structures
Eugenio Bellini
We prove that all left-invariant contact structures on three-dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization pr…