This is the web page of the research group in sub-Riemannian geometry in Padova.
People
- Roberto Monti, Full Professor
- Davide Vittone, Full Professor
- Davide Barilari, Associate Professor
- Valentina Franceschi, Assistant Professsor
- Alessandro Socionovo, PhD student
- Tania Bossio, PhD Student
Research topics
The objectives of the research activity concern some of the most relevant open problems in the field, in particular:
- regularity of geodesics and properties of abnormal curves,
- curvature theory for sub-Riemannian manifolds
- geometric and functional inequalities,
- PDEs of hypoelliptic type arising in the theory
- Geometric Measure Theory
Recent preprints
- R. Monti, A. Socionovo, Non minimality of spirals in sub-Riemannian manifolds Preprint Arxiv 2021.
- A. Julia, S. Nicolussi Golo, D. Vittone, Lipschitz functions on submanifolds in Heisenberg groups Preprint Arxiv 2021.
Some recent research papers relevant to the project
- F. Boarotto, R. Monti, F. Palmurella, Third order open mapping theorems and applications to the end-point map Nonlinearity, 2020
- F. Boarotto, D. Vittone, A dynamical approach to the Sard problem in Carnot groups J. Differential Equations, 2020
- D. Barilari, L. Rizzi, Sub-Riemannian interpolation inequalities. Inventiones Mathematicae, 2019.
- D. Barilari, Y. Chitour, F. Jean, D. Prandi, M. Sigalotti, On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures. Journal de Mathématiques Pures et Appliquées, 2020
- V. Franceschi, D. Prandi, Hardy-type inequalities for the Carnot-Carathéodory distance in the Heisenberg group. Journal of Geometric Analysis, 2020
- V. Franceschi, L. Rizzi, On the essential self-adjointness of singular sub-Laplacians. Potential Analysis, 2020