Research

Research topics:  Geometric Analysis, Isoperimetric  inequalities, Sub-Riemannian geometry, Subelliptic operators, Cortically inspired modelling for vision.

Publications 

1. V. Franceschi, K. Naderi, and K. Pankrashkin, Embedded trace operator for infinite metric trees. accepted on Mathematische Nachrichten [arXiv] 

2. V. Franceschi, R. Monti, and A. Socionovo, Mean value formulas on surfaces in Grushin spaces. Annales Fennici Mathematici, 49(1), 241–255. [arXiv] (doi)

3. V. Franceschi, A. Pinamonti, G. Saracco, G. Stefani, The Cheeger problem in abstract measure spaces. accepted on J. London Math. Society [arXiv] (doi)

4. U. Boscain, D. Cannarsa, V. Franceschi,  M. Sigalotti, Local controllability does imply global controllability. accepted on Comptes Rendus Mathématique. Académie des Sciences. Paris [arXiv] (doi)

5. V. Franceschi, A. Pratelli, G. Stefani, On the Steiner property for planar minimizing clusters. The anisotropic case. J. Éc. polytech. Math., vol. 10, pp. 989–1045, 2023 [arXiv] (doi)

6. B. Cassano, V. Franceschi, D. Krejčiřík, D. Prandi, Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group. Comm. Partial Differential Equations, 48(5):711–752, 2023 [arXiv]  (doi)

7. V. Franceschi, R. Monti, A. Righini, M. Sigalotti, The isoperimetric problem for regular and crystalline norms in  H^1. J. Geom. Anal. vol. 33, no. 1, pp. Paper No. 8, 40, 2023. [arXiv] (doi)

8. V. Franceschi, A. Pratelli, G. Stefani, On the Steiner property for planar minimizing clusters. The isotropic case. Communications in Conteporary Mathematics 25(5):Paper No. 2250040, 29, 2023 [arXiv] (doi)

9. E. Baspinar, L. Calatroni, V. Franceschi, D. Prandi; A cortical-inspired sub-Riemannian model for Poggendorff-type visual illusions, Journal of Imaging. (2021); 7(3):41 [arXiv]  (doi)

10. R. Adami, U. Boscain, V. Franceschi, D. Prandi; Point interactions for 3D sub-Laplacians.  Annales IHP C - Analyse Nonlinéaire vol. 38 (2021), no. 4, 1095–1113. [arXiv] (doi)

11. M. Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, D. Prandi; Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling. Journal of Mathematical Imaging and Vision 63, 263–281 (2021)  [arXiv]  (doi)

12. V. Franceschi, D. Prandi; Hardy-type inequalities for the Carnot-Carathéodory distance in the Heisenberg group. J. Geom. Anal. 31 (2021), no. 3, 2455–2480.  [arXiv]  (doi) 

13. M. Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, A. Gomez Villa, D. Prandi; Visual illusions via neural dynamics: Wilson-Cowan-type models and the efficient representation principle. Journal of Neurophysiology (2020) 123:5, 1606-1618  [arXiv] (doi)

14. V. Franceschi, F. Montefalcone, R. Monti; CMC spheres in the Heisenberg group. Analysis and Geometry in metric spaces 7 (2019), no. 1, 109–129. [arXiv] (doi)

15. M. Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, D. Prandi; A cortical-inspired model for orientation-dependent contrast perception: a link with Wilson-Cowan equations.  SSVM Conference Proceedings, LNCS, Springer (2019).  [arXiv] (doi)

16.  V. Franceschi, D. Prandi, L. Rizzi; Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points. Séminaire de Théorie spectrale et géométrie (Grenoble), 33 (2015-2016), p. 1-15, [.pdf] (doi)

17. V. Franceschi, G. Stefani; Symmetric double bubbles in the Grushin plane. ESAIM Control Optimization Calc. Var., 25 (2019) 77 [arXiv] (doi)

18. V. Franceschi, D. Prandi, L. Rizzi; On the essential self-adjointness of sub-Laplacians. Potential Anal. (2019) [arXiv] (doi)

19.  V. Franceschi; The isoperimetric problem in Carnot-Carathéodory spaces. Bruno Pini Analysis Seminar [S.l.], p. 102-120, may 2018. [.pdf] (doi)

20. V. Franceschi; A minimal partition problem with trace constraint in the Grushin plane. Calc. Var. Partial Differential Equations, 56 (2017), no. [4] [arXiv] (doi)

21. V. Franceschi, and R. Monti; The isoperimetric problem in H-type groups and Grushin spaces, Rev. Mat. Iberoam., 32 (2016), no. [4], 1227-1258. [arXiv] (doi)

22. V. Franceschi , G.P. Leonardi,  and R. Monti; Quantitative isoperimetric inequality in Heisenberg groups, Calc. Var. Partial Differential Equations,  54 (2015), no. [3] 3229-3239 [arXiv] (doi)

Academic works:

• V. Franceschi, Sharp and quantitative isoperimetric inequalities in Carnot-Carathéodory spaces [PhD. Thesis]  [Dissertation slides]

Other:

• V. Franceschi, Isoperimetric Inequalities in Carnot-Carathéodory spaces: from the De Giorgi definition of perimeter to metric geometry. Seminario Dottorato, University of Padova, 2016.  [.pdf]