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., 2024

3. R. Monti and A. Socionovo. Non-minimality of spirals in sub-Riemannian manifolds. Calc. Var. Partial Differential Equations, 60(6):Paper No. 218, 20, 2021.

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.

2. E. Le Donne, N. Paddeu and A. Socionovo. Metabelian distributions and sub-Riemannian geodesics. Preprint arXiv.

3. N. Paddeu and A. Socionovo. Strictly abnormal geodesics with a degeneracy point in the interior of their domain. Preprint arXiv.

4. A. Socionovo. Sharp regularity of sub-Riemannian length-minimizing curves. Preprint arXiv.

With F. Jean and M. Sigalotti. We aim to study higher order Whitney extension theorems in sub-Riemannian geometry and equivalent notions of regularity for the end-point map in Carnot groups (pliability and (H)-condition).

With F. Boarotto, R. Monti, and N. Paddeu. We aim to find new sufficient conditions for abnormal curves to be length minimizing through the study of the second and higher-order differentials of the end-point map. This result may be applied to prove non-smoothness of sub-Riemannian geodesics in the interior of their domain and branching of strictly abnormal geodesics.

With E. Bellini, T. Rossi, and L. Tessarolo. We aim to study the cut-locus of $C^2$ ipersurfaces in sub-Riemannian manifolds, starting from the ideal case.

With T. Rossi and A. Schiavoni Piazza. We aim to prove that sub-Riemannian geodesics may be non-smooth in the interior of their domain and that branching of strictly abnormal geodesics may happens in sub-Riemannian geometry, improving the result in the Preprint 1.