Research

My research interests mainly lie in sub-Riemannian Geometry and Geometric Measure Theory. Currently, I am working on problems concerning the diameter of sub-Riemannian balls in low regularity, the well-posedness of transport and flow equations in Carnot groups, and the theory of Rumin currents in Carnot groups.

Published and accepted papers

•  M. Di Marco, G. Somma, D. Vittone, A note on the diameter of small sub-Riemannian balls, Analysis and Geometry in Metric Spaces 14(1) (2026), 20250037, https://doi.org/10.1515/agms-2025-0037.

Preprints

• G. Somma, S. Verzellesi, D. Vittone, Transport and flow for horizontal Sobolev contact velocities in Carnot groups, available at https://arxiv.org/abs/2609.08738.

• L. Ambrosio, G. Somma, S. Verzellesi, D. Vittone, Renormalization of contact vector fields with horizontal Sobolev regularity in Heisenberg groups, available at https://arxiv.org/abs/2602.00804, submitted.