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Giovanni Catino - Dipartimento di Matematica - Politecnico di Milano
Via Bonardi 9, 20133 Milano, Italy
Tel: +39 02 2399 4615
Office: 524
Email: giovanni<dot>catino<at>polimi<dot>it
Curriculum: eng
Research Interests: Differential and Riemannian Geometry, Partial Differential Equations.
Teaching: WeBeep
Submitted papers:
Liouville Theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster curvature (with D. D. Monticelli, A. Roncoroni, X. Wang), submitted.
Criticality, splitting theorems under spectral Ricci bounds and the topology of stable minimal hypersurfaces (with L. Mari, P. Mastrolia, A. Roncoroni), submitted.
Bach-pinched metrics on closed manifolds (with L. Branca and D. Dameno), submitted.
Published/accepted papers:
Rigidity of solutions to singular/degenerate semilinear critical equations (with D. D. Monticelli, A. Roncoroni), J. Funct. Anal., to appear.
Uniqueness of critical metrics for a quadratic curvature functional (with P. Mastrolia, D.D. Monticelli), J. Math. Pures. Appl. 211 (2026), 103883.
Rigidity of Einstein manifolds with positive Yamabe invariant (with L. Branca, D. Dameno, P. Mastrolia), Ann. Glob. Anal. Geom. 67 (2025), no. 21.
A Liouville theorem in the Heisenberg Group (with Y. Li, D. D. Monticelli, A. Roncoroni), J. Eur. Math. Soc., to appear.
On Riemannian four-manifolds and their twistor spaces: a moving frame approach (with D. Dameno, P. Mastrolia), Math. Nachr. 297 (2024), no 12, 4651-4670.
Some canonical metrics via Aubin's local deformations (with D. Dameno, P. Mastrolia), J. Math. Pures Appl. 191 (2024), 103624.
A closure result for globally hyperbolic spacetimes (with A. Roncoroni), Proc. Amer. Math. Soc. 152 (2024), no. 12, 5339-5354.
Semilinear elliptic equations on manifolds with nonnegative Ricci curvature (with D. D. Monticelli), J. Eur. Math. Soc. 28 (2026), no. 1, 359-392.
On the critical p-Laplace equation (with D. D. Monticelli, A. Roncoroni), Adv. Math. 433 (2023), 109331.
Two rigidity results for stable minimal hypersurfaces (with P. Mastrolia, A. Roncoroni), Geom. Funct. Anal. 34 (2024), 1-18.
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions (with D. Dameno, P. Mastrolia), Ann. Glob. Anal. Geom. 63 (2023).
Rigidity of Critical Metrics for Quadratic Curvature Functionals (with P. Mastrolia, D. D. Monticelli), J. Math. Pures Appl. 171 (2023), 102-121.
Semilinear Li & Yau inequalities (with D. Castorina, C. Mantegazza), Ann. Mat. Pura Appl. 202 (2023), 827-850.
Four dimensional closed manifolds admit a weak harmonic Weyl metric (with P. Mastrolia, D. Monticelli, F. Punzo), Comm. Cont. Math. 25 (2023), no. 8, 2250047.
A matrix Harnack inequality for semilinear heat equations (with G. Ascione, D. Castorina, C. Mantegazza), Math. Ing. 5 (2023), no. 1, 1-15.
Metrics of constant negative scalar-Weyl curvature, Math. Res. Lett. 30 (2023), no. 2, 319-340.
A triviality result for semilinear parabolic equations (with D. Castorina, C. Mantegazza), Math. Ing. 4 (2022), no. 1, 1-15.
A conformal Yamabe problem with potential in the Euclidean space (with F. Gazzola, P. Mastrolia), Ann. Mat. Pura Appl. 200 (2021), 1987-1998.
On the umbilic set of immersed surfaces in three dimensional space forms (with A. Roncoroni, L. Vezzoni), Bull. Sci. Mat. 165 (2020), 102917.
A Weyl Entropy of Pure Spacetime Regions (with F. Belgiorno), Class. Quantum Grav. 37 (2020), 225014.
The Poisson equation on Riemannian manifolds with weighted Poincaré inequality at infinity (with D. Monticelli, F. Punzo), Ann. Mat. Pura Appl. 200 (2021), 791-814.
The Poisson equation on manifolds with positive essential spectrum (with D. Monticelli, F. Punzo), Calc. Var. Partial Differential Equations 58 (2019), no. 4, 146.
A potential generalization of some canonical Riemannian metrics (with P. Mastrolia), Ann. Glob. Anal. Geom. 55 (2019), no. 4, 719-748.
Weyl scalars on compact Ricci solitons (with P. Mastrolia), J. Geom. Anal. 29 (2019), no. 4, 3328-3344.
Rigidity of positively curved shrinking Ricci solitons in dimension four, Geom. Flows 4 (2019), no. 1, 1-8.
Bochner type formulas for the Weyl tensor on four dimensional Einstein manifolds (with P. Mastrolia), Int. Math. Res. Not. (2020) no. 12, 3794-3823.
The Ricci-Bourguignon flow (with L. Cremaschi, C. Mantegazza, Z. Djadli, L. Mazzieri), Pac. J. Math. 287 (2017), no. 2, 337-370.
Integral pinched shrinking Ricci solitons, Adv. Math. 303 (2016), 279-294.
On the geometry of gradient Einstein-type manifolds (with P. Mastrolia, D. Monticelli, M. Rigoli), Pac. J. Math. 286 (2017), no. 1, 39-67.
Gradient Ricci solitons with vanishing conditions on Weyl (with P. Mastrolia, D. Monticelli), J. Math. Pures Appl. 108 (2017), no. 1, 1-13.
A remark on compact hypersurfaces with constant mean curvature in space forms, Bull. Sci. Math. 140 (2016), no. 8, 901-907.
Classification of expanding and steady Ricci solitons with integral curvature decay (with P. Mastrolia, D. Monticelli), Geom. Topol. 20 (2016), no. 5, 2665-2685.
Analytic and geometric properties of generic Ricci solitons (with P. Mastrolia, D. Monticelli, M. Rigoli), Trans. Amer. Math. Soc. 368 (2016), 7533-7549.
Gradient Einstein solitons (with L. Mazzieri), Nonlinear Anal. 132 (2016), 66-94.
On conformally flat manifolds with constant positive scalar curvature, Proc. Amer. Math. Soc. 144 (2016), 2627-2634.
A variational characterization of flat spaces in dimension three (with P. Mastrolia, D. Monticelli), Pac. J. Math. 282 (2016), no. 2, 285-292.
Some rigidity results on critical metrics for quadratic functionals, Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2921-2937.
Conformal Ricci solitons and related integrability conditions (with P. Mastrolia, D. Monticelli, M. Rigoli), Adv. Geom. 16 (2016), no. 3, 301-328.
Locally conformally flat ancient Ricci flows (with C. Mantegazza, L. Mazzieri), Anal. PDE 8 (2015), no. 2, 365-371.
Rigidity of gradient Einstein shrinkers (with L. Mazzieri e S. Mongodi), Comm. Cont. Math. 17 (2015), no. 6, 1550046.
A note on Codazzi tensors (with C. Mantegazza, L. Mazzieri), Math. Ann. 362 (2015), no. 1-2, 629-638.
Critical metrics of the $L^2$-norm of the scalar curvature, Proc. Amer. Math. Soc.142 (2014), 3981-3986.
Bach-flat gradient steady Ricci solitons (with H.-D. Cao, Q. Chen, C. Mantegazza, L. Mazzieri), Calc. Var. Partial Differential Equations 49 (2014) no. 1-2, 125-138.
A note on four dimensional (anti-)self-dual quasi-Einstein manifolds, Differential Geom. Appl. 30 (2012), 660-664.
On the global structure of conformal gradient solitons with nonnegative Ricci tensor (with C. Mantegazza, L. Mazzieri), Comm. Cont. Math. 14 (2012), no. 6, 1250045.
Complete gradient shrinking Ricci solitons with pinched curvature, Math. Ann. 355 (2013), no. 2, 629-635.
Connected sum construction for sigma_k–Yamabe metrics (with L. Mazzieri), J. Geom. Anal. 23 (2013), no. 2, 812-854.
Generalized quasi-Einstein manifolds with harmonic Weyl tensor, Math. Z. 271 (2012), no. 3-4, 751-756.
Locally conformally flat quasi-Einstein manifolds (with C. Mantegazza, L. Mazzieri, M. Rimoldi), J. Reine Angew. Math. 2013 (2013), no. 675, 181-189.
The evolution of the Weyl tensor under the Ricci flow (with C. Mantegazza), Ann. Inst. Fourier 61 (2011), no. 4, 1407-1435.
A sphere theorem on locally conformally flat even-dimensional manifolds (with Z. Djadli, C.B. Ndiaye), Manuscripta Math. 136 (2011), no. 1-2, 237-247.
Integral pinching results for manifolds with boundary (with C.B. Ndiaye), Ann. Sc. Norm. Super. Pisa Cl. Sci. 9 (2010), no. 4, 785-813.
On Perelman’s dilaton (with M. Caldarelli, Z. Djadli, A. Magni, C. Mantegazza), Geom. Ded. 145 (2010), 127-137.
Conformal deformations of integral pinched 3-manifolds (with Z. Djadli), Adv. Math. 223 (2010), no. 2, 393-404.
Books:
Analisi Matematica e Geometria 1 - Esercizi Svolti e Quesiti Teorici (with F. Punzo), II Ed. 2025, Esculapio.
Analisi Matematica e Geometria 2 - Esercizi Svolti e Quesiti Teorici (with F. Punzo), II Ed. 2025, Esculapio.
Esercizi Svolti di Geometria e Algebra Lineare (with S. Mongodi), 2020. Esculapio.
Quesiti a Risposta Multipla di Analisi Matematica 1 (with C. Mantegazza), 2020, Esculapio.
Quesiti a Risposta Multipla di Analisi Matematica 2 (with C. Leone), 2020, Esculapio.
Solved Problems in Calculus 1, 2020, Amazon (.com, .co.uk, .ca, .com.au, .de, .in).
Analysis of Functions, Solved Problems, 2023, Amazon (.com, .co.uk, .ca, .de).
Exercices Corrigés d'Analyse Mathématique et Géométrie 1, 2021, Amazon (.fr).
A Perspective on Canonical Riemannian Metrics (with P. Mastrolia), Progress in Mathematics, vol. 336 (2020), Birkhäuser-Springer.
Introduzione alla Geometria Differenziale e Riemanniana (with P. Mastrolia, A. Roncoroni), 2024, McGraw Hill.
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