My main research interest is about the regularity of geodesics in sub-Riemannian geometry. It has been the main topic of my PhD thesis and it is also the main topic of my actual research activity.

I am also interested in the following research topics: Geometric Measure Theory, Calculus of Variations, Geometric Control Theory, Differential and Riemannian Geometry. 

1.  F. Boarotto, R. Monti, and A. Socionovo. Higher order goh conditions for singular extremals of corank 1. Arch. Rational Mech. Anal., 248(23), 2024. 

2.  V. Franceschi, R. Monti, and A. Socionovo. Mean value formulas on surfaces in Grushin spaces. Ann. Fenn. Math., 49(1), 241–255 (2024).

3. E. Le Donne, N. Paddeu and A. Socionovo. Metabelian distributions and sub-Riemannian geodesics. Advances in Calculus of Variations (2026).

4. R. Monti and A. Socionovo. Non-minimality of spirals in sub-Riemannian manifolds. Calc. Var. Partial Differential Equations, 60, 218 (2021).

5. N. Paddeu and A. Socionovo. Strictly abnormal geodesics with a degeneracy point in the interior of their domain. SIAM Journal Control Opt., 64(2), 580-592 (2026).

6. A. Socionovo. Sharp regularity of sub-Riemannian length-minimizing curves. Calc. Var. Partial Differential Equations, 65, 181 (2026).

1. Y. Chitour, F. Jean, R. Monti, L. Rifford, L. Sacchelli, M. Sigalotti, and A. Socionovo. Not all sub-Riemannian minimizing geodesics are smooth. Preprint arXiv (2025).

2. F. Jean, M. Sigalotti, and A. Socionovo. A note on pliability and the openness of the multiexponential map in Carnot groups. Preprint arXiv (2026).

3. T. Rossi, A. J. Schiavoni Piazza, and A. Socionovo. Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds. Preprint arXiv (2026).