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, like Riemannian manifolds, RCD spaces and Alexandrov spaces. In connection to their properties, I am interested in the study of the isoperimetric problem on these spaces, also by means of tools coming from Geometric Measure Theory and Nonsmooth Geometry. I am also interested in the minimization of extrinsic curvature energies, like the Willmore energy, and in geometric flows of such functionals.
I obtained a PhD in Mathematics in 2020 at Università di Pisa under the supervision of Prof. Matteo Novaga.
For more information see my Curriculum Vitae.
Preprints:
Antonelli G., Pozzetta M., Semola D. : Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature (2024) (arXiv).
Antonelli G., Fogagnolo M., Nardulli S., Pozzetta M. : Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature (2024) (arXiv).
Pascale G., Pozzetta M. : Quantitative isoperimetric inequalities for classical capillarity problems (2024) (arXiv).
Antonelli G., Pozzetta M. : Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature (2023) (arXiv).
Pozzetta M. : Isoperimetry on manifolds with Ricci bounded below: overview of recent results and methods (2023) (arXiv).
Publications:
Antonelli G., Pasqualetto E., Pozzetta M., Semola D. : Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds, Accepted: Ann. Sci. École Norm. Sup. (2022) (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., 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. (2023) (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., Fogagnolo M., Pozzetta M. : The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis Commun. Contemp. Math. (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: Prof. Matteo Novaga, Università di Pisa, 2020.