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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
Published/accepted papers:
Conformal deformations of integral pinched 3-manifolds (with Z. Djadli), Adv. Math. 223 (2010), no. 2, 393-404.
On Perelman’s dilaton (with M. Caldarelli, Z. Djadli, A. Magni, C. Mantegazza), Geom. Ded. 145 (2010), 127-137.
Integral pinching results for manifolds with boundary (with C.B. Ndiaye), Ann. Sc. Norm. Super. Pisa Cl. Sci. 9 (2010), no. 4, 785-813.
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.
The evolution of the Weyl tensor under the Ricci flow (with C. Mantegazza), Ann. Inst. Fourier 61 (2011), no. 4, 1407-1435.
Locally conformally flat quasi-Einstein manifolds (with C. Mantegazza, L. Mazzieri, M. Rimoldi), J. Reine Angew. Math. 2013 (2013), no. 675, 181-189.
Generalized quasi-Einstein manifolds with harmonic Weyl tensor, Math. Z. 271 (2012), no. 3-4, 751-756.
Connected sum construction for sigma_k–Yamabe metrics (with L. Mazzieri), J. Geom. Anal. 23 (2013), no. 2, 812-854.
Complete gradient shrinking Ricci solitons with pinched curvature, Math. Ann. 355 (2013), no. 2, 629-635.
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.
A note on four dimensional (anti-)self-dual quasi-Einstein manifolds, Differential Geom. Appl. 30 (2012), 660-664.
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.
Critical metrics of the $L^2$-norm of the scalar curvature, Proc. Amer. Math. Soc.142 (2014), 3981-3986.
A note on Codazzi tensors (with C. Mantegazza, L. Mazzieri), Math. Ann. 362 (2015), no. 1-2, 629-638.
Rigidity of gradient Einstein shrinkers (with L. Mazzieri e S. Mongodi), Comm. Cont. Math. 17 (2015), no. 6, 1550046.
Locally conformally flat ancient Ricci flows (with C. Mantegazza, L. Mazzieri), Anal. PDE 8 (2015), no. 2, 365-371.
Conformal Ricci solitons and related integrability conditions (with P. Mastrolia, D. Monticelli, M. Rigoli), Adv. Geom. 16 (2016), no. 3, 301-328.
Some rigidity results on critical metrics for quadratic functionals, Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2921-2937.
A variational characterization of flat spaces in dimension three (with P. Mastrolia, D. Monticelli), Pac. J. Math. 282 (2016), no. 2, 285-292.
On conformally flat manifolds with constant positive scalar curvature, Proc. Amer. Math. Soc. 144 (2016), 2627-2634.
Gradient Einstein solitons (with L. Mazzieri), Nonlinear Anal. 132 (2016), 66-94.
Analytic and geometric properties of generic Ricci solitons (with P. Mastrolia, D. Monticelli, M. Rigoli), Trans. Amer. Math. Soc. 368 (2016), 7533-7549.
Classification of expanding and steady Ricci solitons with integral curvature decay (with P. Mastrolia, D. Monticelli), Geom. Topol. 20 (2016), no. 5, 2665-2685.
A remark on compact hypersurfaces with constant mean curvature in space forms, Bull. Sci. Math. 140 (2016), no. 8, 901-907.
Gradient Ricci solitons with vanishing conditions on Weyl (with P. Mastrolia, D. Monticelli), J. Math. Pures Appl. 108 (2017), no. 1, 1-13.
On the geometry of gradient Einstein-type manifolds (with P. Mastrolia, D. Monticelli, M. Rigoli), Pac. J. Math. 286 (2017), no. 1, 39-67.
Integral pinched shrinking Ricci solitons, Adv. Math. 303 (2016), 279-294.
The Ricci-Bourguignon flow (with L. Cremaschi, C. Mantegazza, Z. Djadli, L. Mazzieri), Pac. J. Math. 287 (2017), no. 2, 337-370.
Bochner type formulas for the Weyl tensor on four dimensional Einstein manifolds (with P. Mastrolia), Int. Math. Res. Not. (2020) no. 12, 3794-3823.
Rigidity of positively curved shrinking Ricci solitons in dimension four, Geom. Flows 4 (2019), no. 1, 1-8.
Weyl scalars on compact Ricci solitons (with P. Mastrolia), J. Geom. Anal. 29 (2019), no. 4, 3328-3344.
A potential generalization of some canonical Riemannian metrics (with P. Mastrolia), Ann. Glob. Anal. Geom. 55 (2019), no. 4, 719-748.
The Poisson equation on manifolds with positive essential spectrum (with D. Monticelli, F. Punzo), Calc. Var. Partial Differential Equations 58 (2019), no. 4, 146.
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.
A Weyl Entropy of Pure Spacetime Regions (with F. Belgiorno), Class. Quantum Grav. 37 (2020), 225014.
On the umbilic set of immersed surfaces in three dimensional space forms (with A. Roncoroni, L. Vezzoni), Bull. Sci. Mat. 165 (2020), 102917.
A conformal Yamabe problem with potential in the Euclidean space (with F. Gazzola, P. Mastrolia), Ann. Mat. Pura Appl. 200 (2021), 1987-1998.
A triviality result for semilinear parabolic equations (with D. Castorina, C. Mantegazza), Math. Ing. 4 (2022), no. 1, 1-15.
Metrics of constant negative scalar-Weyl curvature, Math. Res. Lett. 30 (2023), no. 2, 319-340.
A matrix Harnack inequality for semilinear heat equations (with G. Ascione, D. Castorina, C. Mantegazza), Math. Ing. 5 (2023), no. 1, 1-15.
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.
Semilinear Li & Yau inequalities (with D. Castorina, C. Mantegazza), Ann. Mat. Pura Appl. 202 (2023), 827-850.
Rigidity of Critical Metrics for Quadratic Curvature Functionals (with P. Mastrolia, D. D. Monticelli), J. Math. Pures Appl. 171 (2023), 102-121.
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions (with D. Dameno, P. Mastrolia), Ann. Glob. Anal. Geom. 63 (2023).
Two rigidity results for stable minimal hypersurfaces (with P. Mastrolia, A. Roncoroni), Geom. Funct. Anal. 34 (2024), 1-18.
On the critical p-Laplace equation (with D. D. Monticelli, A. Roncoroni), Adv. Math. 433 (2023), 109331.
Semilinear elliptic equations on manifolds with nonnegative Ricci curvature (with D. D. Monticelli), J. Eur. Math. Soc., to appear.
A closure result for globally hyperbolic spacetimes (with A. Roncoroni), Proc. Amer. Math. Soc. 152 (2024), no. 12, 5339-5354.
Some canonical metrics via Aubin's local deformations (with D. Dameno, P. Mastrolia), J. Math. Pures Appl. 191 (2024), 103624.
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.
A Liouville theorem in the Heisenberg Group (with Y. Li, D. D. Monticelli, A. Roncoroni), J. Eur. Math. Soc., to appear.
Rigidity of Einstein manifolds with positive Yamabe invariant (with L. Branca, D. Dameno, P. Mastrolia), Ann. Glob. Anal. Geom. 67 (2025), no. 21.
Submitted papers:
Uniqueness of critical metrics for a quadratic curvature functional (with P. Mastrolia, D.D. Monticelli), submitted.
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.
Rigidity of solutions to singular/degenerate semilinear critical equations (with D. D. Monticelli, A. Roncoroni), submitted.
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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