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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, Gianluca Somma, Davide Vittone,
A note on the diameter of small sub-Riemannian balls.
Anal. Geom. Metr. Spaces 14 (2026), no. 1, Paper No. 20250037, 8 pp., https://doi.org/10.1515/agms-2025-0037.
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, Mikaela Iacobelli,
Quantization of measures in Carnot groups.
Preprint (2026) available online at https://arxiv.org/abs/2606.09373, submitted.
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.
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". (Proceedings of the "Winter School in Geometric Measure Theory", held in Hangzhou, China, 2025).
Marco Di Marco,
Stokes’ Theorem in Heisenberg groups.
To appear in the proceedings of the conference “Geometric Measure Theory and applications 2024”, held in Cortona, Italy, 2024. The proceedings will be published in the Springer INdAM Series.
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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