My research activity focuses on Geometric Analysis and it is often motivated by variational problems. I am interested in analytic and geometric properties of spaces with curvature bounds, and in the isoperimetric properties of these spaces. I also work on quantitative geometric and functional inequalities, geometric flows and extrinsic curvature energies.
Preprints
Carazzato D., Pascale G., Pozzetta M. : Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms (2025) (arXiv).
Antonelli G., Pozzetta M., Xu K. : A sharp spectral splitting theorem (2024) (arXiv).
Benatti L., Pluda A., Pozzetta M. : Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas (2024) (arXiv).
Antonelli G., Fogagnolo M., Nardulli S., Pozzetta M. : Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature (2024) (arXiv).
Publications
Antonelli G., Pozzetta M., Semola D. : Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature, Comm. Pure Appl. Math. 78 (2025), no. 9, 1656–1702. (arXiv).
Antonelli G., Pozzetta M. : Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature J. Funct. Anal. 289 (2025), no. 4, Paper No. 110940 (arXiv).
Antonelli G., Pasqualetto E., Pozzetta M., Semola D. : Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds, Ann. Sci. Éc. Norm. Supér. 58 (2025), no. 1, 1-52 (arXiv).
Antonelli G., Pasqualetto E., Pozzetta M., Violo I. Y. :Topological regularity of isoperimetric sets in PI spaces having a deformation property, Proc. R. Soc. Edinb., Sect. A, Math. 155 (2025), no. 2, 611–633. (arXiv).
Pascale G., Pozzetta M. : Quantitative isoperimetric inequalities for classical capillarity problems, Calc. Var. 63, 225 (2024) (arXiv).
Antonelli G., Pasqualetto E., Pozzetta M., Semola D. : Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds, Math. Ann. 389, 1677–1730 (2024) (arXiv).
Pluda A., Pozzetta M. : Lojasiewicz-Simon inequalities for minimal networks: stability and convergence, Math. Ann. 389, 2729–2782 (2024) (arXiv).
Antonelli G., Fogagnolo M., Pozzetta M. : The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis Commun. Contemp. Math. 26 (2024), no. 1, Paper No. 2250068 (arXiv).
Pozzetta M. : Isoperimetry on manifolds with Ricci bounded below: overview of recent results and methods (2024) Conference Proceedings in "Anisotropic Isoperimetric Problems and Related Topics" (arXiv).
Pluda A., Pozzetta M. : Minimizing properties of networks via global and local calibrations, Bull. London Math. Soc. 55 (2023), no. 6, 3029–3052 (arXiv).
Pozzetta M. : Confined Willmore energy and the Area functional, Comm. Anal. Geom., Volume 31, Number 2, 407-447, 2023 (arXiv).
Antonelli G., Bruè E., Fogagnolo M., Pozzetta M. : On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth, Calc. Var. 61, 77 (2022) (arXiv).
Antonelli G., Nardulli S., Pozzetta M. : The isoperimetric problem via direct method in noncompact metric measure spaces with lower Ricci bounds, ESAIM: COCV 28 (2022) 57 (arXiv).
Antonelli G., Pasqualetto E., Pozzetta M. : Isoperimetric sets in spaces with lower bounds on the Ricci curvature, Nonlinear Anal. Volume 220, 2022, 112839 (arXiv).
Dayrens F., Masnou S., Novaga M., Pozzetta M. : Connected perimeter of planar sets, Adv. Calc. Var., vol. 15, no. 2, 2022, pp. 213-234 (arXiv).
Mantegazza C., Pozzetta M. : Asymptotic convergence of evolving hypersurfaces, Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 1927–1944 (arXiv).
Pozzetta M. : Convergence of elastic flows of curves into manifolds, Nonlinear Anal. Volume 214, 2022, 112581 (arXiv).
Del Nin G., Pluda A., Pozzetta M. : Degenerate elastic networks, J. Geom. Anal. 31, 6128-6170 (2021) (arXiv).
Mantegazza C., Pluda A., Pozzetta M. : A survey of the elastic flow of curves and networks, Milan J. Math. 89, 59-121 (2021) (arXiv).
Mantegazza C., Pozzetta M. : The Lojasiewicz-Simon inequality for the elastic flow, Calc. Var. 60, 56 (2021) (arXiv).
Pozzetta M. : On the Plateau-Douglas problem for the Willmore energy of surfaces with planar boundary curves, ESAIM: COCV 27 (2021) S2 (arXiv).
Novaga M., Pozzetta M. : Connected surfaces with boundary minimizing the Willmore energy, Math. Eng., 2020, 2(3): 527-556. (arXiv).
Pozzetta M. : A varifold perspective on the p-elastic energy of planar sets, J. Conv. Anal. 27 (2020), No. 3, 845-879 (arXiv).
Unpublished
Pluda A., Pozzetta M. : On the uniqueness of nondegenerate blowups for the motion by curvature of networks (2022) (arXiv).
PhD Thesis: "Willmore-type Energies of Curves and Surfaces", Supervisor: Matteo Novaga, Università di Pisa, 2020.