Homepage di Giovanni Catino
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
Books:
Esercizi Svolti di Analisi Matematica e Geometria 1 (with F. Punzo), 2020, Esculapio.
Esercizi Svolti di Analisi Matematica e Geometria 2 (with F. Punzo), 2020, Esculapio.
Esercizi Svolti di Analisi Matematica e Geometria 1 e 2 (with F. Punzo), 2020, Esculapio.
Esercizi Svolti di Geometria e Algebra Lineare (with S. Mongodi), 2020. Esculapio.
Quesiti Teorici di Analisi Matematica e Geometria 1 (with F. Punzo), 2020, Esculapio.
Quesiti Teorici di Analisi Matematica e Geometria 2 (with F. Punzo), 2020, Esculapio.
Quesiti Teorici di Analisi Matematica e Geometria 1 e 2 (with F. Punzo), 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.
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 and 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 and 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 and 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 and 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 and 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 and 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 and L. Mazzieri), Anal. PDE 8 (2015), no. 2, 365-371.
Conformal Ricci solitons and related integrability conditions (with P. Mastrolia, D. Monticelli and 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 and 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 and M. Rigoli), Trans. Amer. Math. Soc. 368 (2016), 7533-7549.
Classification of expanding and steady Ricci solitons with integral curvature decay (with P. Mastrolia and 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 and 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 and 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 and 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 and 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 and L. Vezzoni), Bull. Sci. Mat. 165 (2020), 102917.
A conformal Yamabe problem with potential in the Euclidean space (with F. Gazzola and P. Mastrolia), Ann. Mat. Pura Appl. 200 (2021), 1987-1998.
A triviality result for semilinear parabolic equations (with D. Castorina and 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 and F. Punzo), Comm. Cont. Math. 25 (2023), no. 8, 2250047.
Semilinear Li & Yau inequalities (with D. Castorina and 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), no. 9, 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.
Submitted papers:
On Riemannian four-manifolds and their twistor spaces: a moving frame approach (with D. Dameno and P. Mastrolia), submitted.
Some canonical metrics via Aubin's local deformations (with D. Dameno, P. Mastrolia), submitted.
Uniqueness of critical metrics for a quadratic curvature functional (with P. Mastrolia, D.D. Monticelli), submitted.
A closure result for globally hyperbolic spacetimes (with A. Roncoroni), submitted.
A Liouville theorem in the Heisenberg Group (with Y. Li, D. D. Monticelli, A. Roncoroni), submitted.
Rigidity of Einstein manifolds with positive Yamabe invariant (with L. Branca, D. Dameno and P. Mastrolia), submitted.
Links: MathSciNet, ArXiv, CVGMT, Scholar