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Main research interests:
During my PhD studies I focused on Sub-Riemannian Geometry, Geometric Measure Theory, Calculus of Variations; in more detail: submanifolds and currents in Carnot groups, BV functions in Carnot-Carathéodory spaces, differentiability of Lipschitz maps in metric measure spaces, relationship between contact and sub-Riemannian geometry. Currently I am also interested in Quantization of Measures and Optimal Transport.
Published and accepted papers:
Marco Di Marco, Sebastiano Don, Davide Vittone,
SBV functions in Carnot-Carathéodory spaces.
Nonlinear Anal. 262 (2026), Paper No. 113944, 20 pp., https://doi.org/10.1016/j.na.2025.113944.
Marco Di Marco, Andrea Pinamonti, Davide Vittone, Kilian Zambanini,
Stepanov differentiability theorem for intrinsic graphs in Heisenberg groups.
Adv. Calc. Var. 18 (2025), no. 3, 963-978, https://doi.org/10.1515/acv-2024-0118.
Marco Di Marco, Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone,
Submanifolds with boundary and Stokes' Theorem in Heisenberg groups.
Trans. Amer. Math. Soc. 378 (2025), no. 7, 4955-4990, https://doi.org/10.1090/tran/9410.
Preprints:
Marco Di Marco,
Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces.
Preprint (2025) available online at https://arxiv.org/abs/2510.19380, submitted.
Marco Di Marco, Gianluca Somma, Davide Vittone,
A note on the diameter of small sub-Riemannian balls.
Preprint (2025) available online at https://arxiv.org/abs/2505.02790, submitted.
Proceedings:
Marco Di Marco, Davide Vittone,
Submanifolds with boundary in sub-Riemannian Heisenberg Groups.
Preprint (2025) available online at https://arxiv.org/abs/2508.15634, submitted to to the series "Actes et Congrès" of the "Société Mathématique de France".
PhD Thesis:
Marco Di Marco,
Euclid meets Heisenberg.
Università degli Studi di Padova, 2025.
Supervisor: Davide Vittone.
Cosupervisor: Antoine Julia.
Referees: Luca Capogna, Pierre Pansu.
Phd Thesis available online at https://cvgmt.sns.it/paper/7411/.
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