Research

Publications

  1. F. Essebei, G. Giovannardi, S. Verzellesi, Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups. Nonlinear Differ. Equ. Appl. 31, 95 (2024). https://doi.org/10.1007/s00030-024-00983-y
  2. G. Giovannardi, J. Pozuelo, A. Pinamonti, S. Verzellesi , The prescribed mean curvature equation for t-graphs in the sub-Finsler Heienberg group ℍ^n. Adv. in Math. 451  (2024) https://doi.org/10.1016/j.aim.2024.109788.
  3. G. Citti, G. Giovannardi, Y. Sire, Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential. Ann. Sc. Norm. Super. Pisa Cl. Sci. (to appear) arXiv:2104.08115.(2024).
  4. F. Dragoni, N. Garofalo, G. Giovannardi, P. Salani, A fundamental solution for a subelliptic operator in Finsler geometry.  Indiana Univ. Math. J. (to appear)  arXiv:2401.06736 (2024).
  5. L. Capogna, G. Giovannardi, A. Pinamonti, S. Verzellesi, The asymptotic p-Poisson equation as p->+\infty in Carnot Carathéodory spaces.  Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02805-z
  6. G. Giovannardi, M. Ritoré, The Bernstein problem for (X,Y)-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups Commun. Contemp. Math. Vol. 26, No. 09, 2350048 (2024). https://doi.org/10.1142/S0219199723500487
  7. G. Giovannardi, J. Pozuelo, M. Ritoré, Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group ℍ^1. In: Alarcón, A., Palmer, V., Rosales, C. (eds) New Trends in Geometric Analysis. RSME Springer Series, vol 10. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-39916-9_7
  8. G. Giovannardi, D. Mugnai, E. Vecchi, An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems, Journal of Mathematical Analysis and Applications, 527, no. 2 (2023). https://doi.org/10.1016/j.jmaa.2023.127442.
  9. G. Giovannardi, The sub-Finsler Bernstein problem in H^1, Bruno Pini Mathematical Analysis Seminar, 13(1), (2023), 68-89. https://doi.org/10.6092/issn.2240-2829/16158
  10. G. Citti, G. Giovannardi, M. Ritoré, Variational formulas for curves of fixed degree, Advances in Differential Equations, Volume 27, Numbers 5-6 (2022), 333-384.
  11. S. E.-Bique, G. Giovannardi, R. Korte, N. Shanmugalingam, G. Speight, Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry, Journal of Differential Equations, Volume 306 (2022), 590-632. https://doi.org/10.1016/j.jde.2021.10.029.
  12. G. Giovannardi, M. Ritoré, Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group ℍ^1, Journal of Differential Equations (2021), Volume 302, 474-495. https://doi.org/10.1016/j.jde.2021.08.040
  13. G. Citti, G. Giovannardi, M. Ritoré, Variational formulas for submanifolds of fixed degree. Calc. Var. 60, 233 (2021). https://doi.org/10.1007/s00526-021-02100-8.
  14. G. Citti, G. Giovannardi, M. Ritoré, A. Sarti, Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion, Nielsen F., Barbaresco F. (eds) Geometric Science of Information, GSI 2021, Lecture Notes in Computer Science, vol 1282.  https://doi.org/10.1007/978-3-030-80209-7_6
  15. G. Giovannardi, Higher dimensional holonomy map for ruled submanifolds in graded manifolds, Analysis and Geometry in Metric Spaces (2020), Volume 8, no.1, 68-91. https://doi.org/10.1515/agms-2020-01

Preprints

  1. G. Giovannardi, A. Pinamonti, S. Verzellesi, Curvature estimates for minimal hypersurfaces in the Heisenberg group, arXiv:2409.20359 (2024).

Communications

  1. June 2017: Introduction to sub-Riemannan geometry with some applications to the primary visual cortex, Seminario de Jóvenes Investigadores en Matemáticas, IEmath, Univeristy of Granada.
  2. March 2018: A notion of area for immersed submanifolds in a sub-Riemannian geometry, Special Seminar in Geometric Analysis, Fine Hall, Princeton University.
  3. July 2019: Variations for curves, Bad Seminar, Department of Mathematics, University of Bologna.
  4. September 2019: Variations for submanifolds of fixed degree, Poster section, Geometric Analysis, Submanifolds and Geometry of PDEs, Torino.
  5. September 2019: Variations for submanifolds in graded manifolds, Short talk, Shape Optimization and Isoperimetric and Functional Inequalities, Levico Terme.
  6. November 2019: Variations for submanifolds in graded manifolds, Simons Semester, IMPAN, room 321, Warsaw, November 15th 2019.
  7. March 2020: Variations for submanifolds in graded manifolds, PDE and Analysis Seminar, 427 Thackeray Hall, University of Pittsburgh.
  8. Febraury 2021: Variations for curves in graded manifold, Seminario de Jóvenes Investigadores en Matemáticas, IEmath, Univeristy of Granada.
  9. March 2021: Regularity of Lipschitz boundaries with prescribed sub- Finsler mean curvature in the first Heisenberg group, Virtual IMUS Seminar: Problemas variacionales geométricos y teoría del potencial Serie, IMUS, Universidad de Sevilla.
  10. May 2021: The Bernstein problem for Euclidean Lipschitz surfaces in the sub-Finsler Heisenberg group H^1, Geometry Seminar of the University of Granada, Deparment of Geometry and Topology, Univeristy of Granada.
  11. October  2021, The Bernstein problem for Euclidean Lipschitz surfaces in the sub-Finsler Heisenberg group H^1, Seminario periodico del Dipartimento di Matematica, University of Trento.
  12. December 2021, The Bernstein problem for Euclidean Lipschitz surfaces in the sub-Finsler Heisen- berg group H1, Seminario di Analisi Matematica Bruno Pini, University of Bologna.
  13. January 2022, Variations for submanifolds in graded manifolds, Section of Geometric Analysis, Congreso Bienal de la Real Sociedad Matematica Española, Ciudad Real
  14. November 2022, Minimal and CMC surfaces in the sub-Finsler Heisenberg group H^1,Seminario di Analisi Matematica, DIMAI Dipartimento di Matematica e Informatica "Ulisse Dini", Firenze.
  15. May 2023, Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential, XXXII Convegno Nazionale di Calcolo delle Variazioni, Levico Terme.
  16. June 2023, Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential, NonPUB23 - Nonlocal and Nonlinear Partial Differential Equations, University of Bologna.
  17. July 2023, Minimal and CMC surfaces in the sub-Finsler Heisenberg group. Sub-Riemannian Geometry Harmonic Analysis, PDEs and Applications, University of Bologna.
  18.  July 2024, The prescribed mean curvature equation for t-graphs in the sub-Finsler Heisenberg group H^n, 9th European Congress of Mathematics, Special section: Geometric and regularity aspects of sub-elliptic PDEs, Sevilla.
  19. July 2024, The asymptotic p-Poisson equation as p->+ \infty in Carnot-Carathéodory spaces, AMS-UMI Joint Meeting, Advances in Geometric Control Theory and Subelliptic PDEs, Special Session A16, Palermo.


© 2019 Gianmarco Giovannardi. Tutti i diritti riservati.
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