The title links to the published version of the papers, when available, while [.pdf] links to the preprint version. All preprints are also available on the French archive HAL.
MONOGRAPHS AND BOOKS
SLIDES AND VIDEOS OF SOME PAST TALKS
- A Comprehensive Introduction to Sub-Riemannian Geometry (with A. Agrachev and U. Boscain), Book, Accepted for Cambridge University Press (preprint version 08/11/2018). [.pdf]
- Curvature: a variational approach (with A. Agrachev and L. Rizzi), [Cover]Memoirs of the AMS, 256 (2018), no. 1225, vi + 142 pp. [.pdf]
- Introduction to geodesics in sub-Riemannian geometry (with A. Agrachev and U. Boscain), [Cover]in "Geometry, Analysis and Dynamics in SR manifolds, vol.II", EMS Lecture Notes series (2016), 85pp., DOI 10.4171/163-1/1.
- On the Hausdorff volume in sub-Riemannian geometry (with A. Agrachev and U. Boscain), Calculus of Variations and PDE, 43 (2012), no. 3-4, 355-388. [.pdf]
- Sub-Riemannian structures on 3D Lie groups (with A. Agrachev), Journal of Dynamical and Control Systems (2012), 18: 21-44. [.pdf]
- Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry, Journal of Mathematical Sciences, 195 (2013), no. 3, 391-411. [.pdf]
- On 2-step, corank 2 sub-Riemannian metrics (with U. Boscain and J.P. Gauthier), SIAM Journal of Control and Optimization, 50 (2012), no. 1, 559-582. [.pdf]
- Small time heat kernel asymptotics at the sub-Riemannian cut locus (with U. Boscain and R.W. Neel), Journal of Differential Geometry, 92 (2012), no.3, 373-416. [.pdf]
- A formula for Popp's volume in sub-Riemannian geometry (with L. Rizzi), Analysis and Geometry in Metric Spaces, 1 (2013), 42-57. [.pdf]
- Small time heat kernel asymptotics at the cut locus on surfaces of revolution (with J. Jendrej), Annales Institut Henri Poincaré - Analyse Non Linéaire, 31 (2014), pp. 281-295. [.pdf]
- Comparison theorems for conjugate points in sub-Riemannian geometry (with L. Rizzi), ESAIM: COCV v.22, n.2 (2016) 439-472. [.pdf]
- Sub-Riemannian curvature in contact geometry (with A. Agrachev and L. Rizzi), The Journal of Geometric Analysis (2017) 27: 366-408. [.pdf]
- On the heat diffusion for generic Riemannian and sub-Riemannian structures (with U. Boscain, R.W. Neel and G. Charlot), International Mathematics Research Notices (2017) 15: 4639-4672. [.pdf]
- On Jacobi fields and canonical connection in sub-Riemannian geometry (with L. Rizzi). Archivum Mathematicum, 53 (2017), 77-92. [.pdf]
- Sub-Finsler structures from the time-optimal viewpoint on some nilpotent distributions (with U. Boscain, E. Le Donne, M. Sigalotti), Journal of Dynamical and Control Systems (2017) 23: 547-575. [.pdf]
- Heat kernel asymptotics on SR manifolds with symmetries, applications to the bi-Heisenberg group (with U. Boscain, R.W. Neel). Annales de la Faculté des Sciences de Toulouse, accepted. [.pdf]
- Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators (with E. Paoli). Nonlinear Analysis, 164 (2017) 118-134. [.pdf]
- Sharp measure contraction property for generalized H-type Carnot groups (with L. Rizzi). Communications in Contemporary Mathematics, 20 (2018), no. 06, 1750081. [.pdf]
- On the set of points of smoothness for the value function of affine optimal control problems (with F. Boarotto). SIAM Journal of Control and Optimization, 56 (2018), no. 2, 649–671. [.pdf]
- Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature (with F. Boarotto). Journal of Evolution Equations, 18 (2018), no. 3, 1115-1146. [.pdf]
- Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics (with A. Agrachev, E. Paoli). Annales de l'Institut Fourier, accepted. [.pdf]
- Sub-Riemannian interpolation inequalities (with L. Rizzi). Inventiones Mathematicae, (2018). https://doi.org/10.1007/s00222-018-0840-y. [.pdf]
- On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures (with Y. Chitour, F. Jean, D. Prandi, M. Sigalotti). Journal de Mathématiques Pures et Appliquées, accepted. [.pdf]
- A Bonnet-Myers type theorem for quaternionic contact structures (with S. Ivanov). Calculus of Variations and PDE, (2019) 58: 37. [.pdf]
- Volume of small balls and sub-Riemannian curvature in 3D contact manifolds. (with I. Beschastnyi, A. Lerario). Journal of Symplectic Geometry, accepted. [.pdf]
- Geometry of Maslov cycles (with A. Lerario). Geom. Control and SR Geometry. Springer INDAM Series, 15-35, vol. 5 (2014). [.pdf]
- Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution (with U. Boscain, E. Le Donne and M. Sigalotti), Proceedings of the 54th IEEE CDC, Osaka, Japan, Dec 2015. [.pdf]
- Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes (with U.Boscain, G.Charlot and R.Neel). Actes du séminaire de Théorie spectrale et géométrie, Grenoble, Volume 31 (2012-2014), 55-70. [.pdf]
- D. Barilari, U. Boscain, M. Sigalotti, editors. (2016) - EMS Series of Lectures in Mathematics "Dynamics, geometry and analysis on sub-Riemannian manifolds", Volume I. 332 pages. "Dynamics, geometry and analysis on sub-Riemannian manifolds", Volume II. 307 pages.
SLIDES AND VIDEOS OF SOME PAST TALKS
- On the Brunn-Minkovski inequality in sub-Riemannian geometry
at Riemannian Geometry and Generalized Functions, Paris, France, October 2018
- On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures
at Sub-Riemannian Geometry and Topolo(gy), Topolo, Italy, June 2018
- On the regularity of the value function for affine optimal control problems
at Mathematical Control Theory, Porquerolles, France, June 2017
- From Thermodynamics to Image Reconstruction: an invitation to sub-Riemannian geometry
at Mathematics and Phisycs Colloquium, Hannover, November 2016
- Volume geodesic distortion and Ricci curvature in sub-Riemannian geometry - [Video]
at Journée ANR "On the sub-Riemannian Laplacian", Grenoble, October 2016
- Sub-Riemannian curvature: a variational approach
at Workshop "Geometric Analysis on sub-Riemannian manifolds", IHP, Paris, September 2014
- Heat kernel asymptotics at the cut locus on Riemannian and sub-Riemannian manifolds - [Video]
at "International Youth Conference "Geometry & Control", Steklov Institute, Moscow, April 2014
- Comparison theorems for conjugate points in sub-Riemannian geometry
at Workshop "Analysis and Geometry in Control Theory and applications", INDAM, Rome, June 2014
- [Ph.D. Thesis] Invariants, Volumes and Heat Kernels in sub-Riemannian geometry.
Supervisor: Andrei Agrachev. SISSA, Trieste. Defended on 27/10/2011.
SISSA "Lutman Prize" for the Best Ph.D. Thesis in Mathematics, 2012
- [Master Thesis] Sub-Riemannian structures on three dimensional Lie groups.
Supervisor: Andrei Agrachev. Università degli Studi di Trieste and SISSA.