I am an Assistant Professor (RTT) at the Department of Mathematics of the Politecnico di Milano. I received my PhD in Mathematics from the University of Pavia in 2019. Before joining the Politecnico di Milano in 2022, I held postdoctoral positions at the University of Florence (Italy) and the University of Granada (Spain).
My research lies at the interface between differential geometry and partial differential equations, with particular emphasis on rigidity phenomena, geometric inequalities, minimal surfaces, and nonlinear elliptic equations.
D. Castorina, G. Catino, C. Mantegazza, A. Roncoroni. A Liouville theorem for semilinear parabolic critical equations. Submitted
G. Catino, D. D. Monticelli, A. Roncoroni. Quasilinear Liouville equation on manifolds with nonnegative Ricci curvature. Submitted [preprint]
G. Catino, L. Mari, P. Mastrolia, A. Roncoroni. Criticality, splitting theorems under spectral Ricci bounds and the topology of stable minimal hypersurfaces. Submitted [preprint]
G. Catino, D. D. Monticelli, A. Roncoroni, X. Wang. Liouville theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster-Ricci curvature. Submitted [preprint]
X. Cabré, G. Catino, L. Mari, P. Mastrolia, A. Roncoroni. Gradient estimates for the Green kernel under spectral Ricci bounds, and the stable Bernstein problem in R^4. Trans. Amer. Math. Soc. To appear [preprint, journal]
G. Catino, D. D. Monticelli, A. Roncoroni. Rigidity of solutions to singular/degenerate semilinear equations. J. Funct. Anal. 291 (2026) 111538 [preprint, journal]
A. Grigor'yan, G. Meglioli, A. Roncoroni. Rigidity for the heat equation with density on Riemannian manifolds through a conformal change. Proc. Roy. Soc. Edinburgh Sect. A. Published online 2026, 1-41. [preprint, journal]
G. Catino, Y. Y. Li, D. D. Monticelli, A. Roncoroni. A Liouville theorem in the Heisenberg group. J. Eur. Math. Soc. (2025) published online first. [preprint, journal]
S. Biagi, F. Esposito, A. Roncoroni, E. Vecchi. A Brezis-Nirenberg type result for the anisotropic p-Laplacian. J. London Math. Soc. (2) 2025, 112. [preprint, journal]
G. Catino, A. Roncoroni. A closure result for globally hyperbolic spacetimes. Proc. Amer. Math. Soc. 152 (2024), 5339-5354 [preprint, journal]
F. Pacella, G. Poggesi, A. Roncoroni. Optimal quantitative stability for a Serrin-type problem in convex cones. Math. Z. 307, 79 (2024) [preprint, journal]
A. Freitas, A. Roncoroni, M. Santos. A note on Serrin's type problem on Riemannian manifolds. J. Geom. Anal. 34, 200 (2024). [preprint, journal]
G. Catino, P. Mastrolia, A. Roncoroni. Two rigidity results for stable minimal hypersurfaces. Geom. Funct. Anal. 34, 1-18 (2024). [preprint, journal]
G. Catino, D. D. Monticelli, A. Roncoroni. On the critical p-Laplace equation. Adv. Math. 433 (2023), 109331. [preprint, journal]
G. Meglioli, A. Roncoroni. Uniqueness in weighted Lebesgue spaces for an elliptic equation with drift on manifolds. J. Geom. Anal. 33, 320 (2023). [preprint, journal]
G. Ciraolo, R. Corso, A. Roncoroni. Non-existence of patterns for a class of weighted degenerate operators. J. Differential Equations 370 (2023), 240-270. [preprint, journal]
A. Roncoroni. Liouville-type results for the Lane-Emden equation. Bruno Pini Mathematical Analysis Seminar, vol. 14, issue 1 (2023), 77-94. [journal]
C. Bianchini, A. Colesanti, D. Pagnini, A. Roncoroni. On p-Brunn-Minkowski inequalities for intrinsic volumes, with 0≤p<1. Math. Ann. 387, 321-352 (2023). [preprint, journal]
A. Roncoroni. An overview on extremals and critical points of the Sobolev inequality in convex cones. Rend. Lincei Mat. Appl. 33 (2022), 967-995. [preprint, journal]
M. Muratori, A. Roncoroni. Sobolev-type inequalities on Cartan-Hadamard manifolds and applications to some nonlinear diffusion equations. Potential Anal. 57, 129-154 (2022). [preprint, journal]
A. Farina, A. Roncoroni. A note on Serrin’s problem in warped product manifolds. Comm. Cont. Math. (2021) 2150020 (21 pages). [preprint, journal]
G. Ciraolo, R. Corso, A. Roncoroni. Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions. J. Funct. Anal. 280 (2021), 108787. [preprint, journal]
G. Ciraolo, A. Roncoroni, L. Vezzoni. Quantitative stability for hypersurfaces with almost constant curvature in space forms. Ann. Mat. Pura Appl. 200 (2021), 2043-2083. [preprint, journal]
G Catino, A. Roncoroni, L. Vezzoni. On the umbilic set of immersed surfaces in three-dimensional space forms. Bull. Sci. Math. 165 (2020) 102917. [preprint, journal]
G. Ciraolo, A. Figalli, A. Roncoroni. Symmetry results for critical anisotropic p-Laplace equations in convex cones. Geom. Funct. Anal. 30, 770-803 (2020). [preprint, journal]
G. Ciraolo, A. Roncoroni. Serrin’s type overdetermined problems in convex cones. Calc. Var. 59, 28 (2020). [preprint, journal]
G. Ciraolo, A. Roncoroni. The method of moving planes: a quantitative approach. Bruno Pini Mathematical Analysis Seminar, vol. 9 (2018) pp. 41-77. [preprint, journal]
A. Roncoroni. A Serrin-type symmetry result on model manifolds: an extension of the Weinberger argument. C. R. Math. Acad. Sci. Paris, 356 (2018), no. 6, 648–656. [preprint, journal]
Bridging Analysis and Geometry, Politecnico di Milano, December 14, 2026.
Late Summer Conference in Geometric Analysis, Università di Padova, August 30-September 3, 2026.
Reading seminar in Geometric Analysis, with Marco Pozzetta. Held at Politecnico di Milano (Italy) in Fall 2025 and Spring 2026.
Perspectives in Geometric Analysis, Politecnico di Milano, September 8-11, 2025.
Differential Geometry @ L'Aquila, Università dell'Aquila, June 30-July 4, 2025.
PRIN Meeting "Differential-geometric aspects of manifolds via Global Analysis", Università di Torino, June 17-18, 2024.
New Trends in Geometric & Variational PDEs, Università di Trento, February 20-22, 2023.
Geometric Analysis and PDEs at PoliMi, Politecnico di Milano, December 5, 2022.
An introduction to Differential and Riemannian Geometry for students in Mathematics, Physics, and Engineering.