75 citations · 484 across the 32 of their papers we have counts for
35 papers
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…
Steiner and tube formulae in 3D contact sub-Riemannian geometry
Davide Barilari, Tania Bossio
We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain,…
Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures
Davide Barilari, Andrea Mondino, Luca Rizzi
Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannia…
Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold
Davide Barilari, Karen Habermann
We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact sub-Riemannian manifold. We pr…
Spectral summability for the quartic oscillator with applications to the Engel group
Hajer Bahouri, Davide Barilari, Isabelle Gallagher +1
In this article, we investigate spectral properties of the sublaplacian on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approac…