Carlo Mantegazza Mathematical Analysis Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" Università degli Studi di Napoli Federico II Scuola Superiore Meridionale Via Cintia, Monte S. Angelo I-80126 Napoli, Italy Email: carlo.mantegazza@unina.it Office: +39/081/675751

Dipartimento di Matematica e Applicazioni Renato Caccioppoli

Course at the Università di Napoli Federico II, Matematica - Geometria Riemanniana
Course at the Università di Napoli Federico II, Matematica - Misura e Integrazione secondo Lebesgue (with Flavia Giannetti)
Course at the Università di Napoli Federico II, Biologia - Matematica (with Giusy Terzo)
Course at the Scuola Superiore Meridionale, I Anno - Complementi di Matematica (with Pietro Baldi)

Luca Benatti, Carlo Mantegazza, Francesca Oronzio and Alessandra Pluda
A Note on Ricci-pinched 3-Manifolds, Preprint, 2024.

Antonia Diana, Nicola Fusco and Carlo Mantegazza
Stability for the Surface Diffusion Flow, Preprint, 2023.

Virginia Agostiniani, Carlo Mantegazza, Lorenzo Mazzieri and Francesca Oronzio
Riemannian Penrose Inequality via Nonlinear Potential Theory, Preprint, 2022.

Riccardo Benedetti and Carlo Mantegazza
La Congettura di Poincaré, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 102, 2024.

Serena Della Corte, Antonia Diana and Carlo Mantegazza
Uniform Sobolev, Interpolation and Geometric Calderón-Zygmund Inequalities for Graph Hypersurfaces, Note di Matematica 44, 53-83, 2024.

Carlo Mantegazza, Matteo Novaga, Alessandra Pluda and Felix Schulze
Evolution of Networks with Multiple Junctions, Astérisque 452, 2024.

Virginia Agostiniani, Carlo Mantegazza, Lorenzo Mazzieri and Francesca Oronzio
A New Proof of the Riemannian Penrose Inequality, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 34, 715-726, 2023.

Daniele Castorina, Giovanni Catino and Carlo Mantegazza
Semilinear Li & Yau Inequalities, Ann. Mat. Pura Appl. 202, 827-850, 2023.

Giacomo Ascione, Daniele Castorina, Giovanni Catino and Carlo Mantegazza
A Matrix Harnack Inequality for Semilinear Heat Equations, Math. Engineering 5, 2023.

Carlo Mantegazza, Matteo Novaga and Alessandra Pluda
Type-0 Singularities in the Network Flow - Evolution of Trees, J. Reine Angew. Math. (Crelle's Journal) 792, 189-221, 2022.

Carlo Mantegazza and Marco Pozzetta
Asymptotic Convergence of Evolving Hypersurfaces, Rev. Mat. Iberoam. 38, 1927-1944, 2022.

Serena Della Corte, Antonia Diana and Carlo Mantegazza
Global Existence and Stability for the Modified Mullins-Sekerka and Surface Diffusion Flow, Math. Engineering 4, 2022.

Daniele Castorina, Giovanni Catino and Carlo Mantegazza
A Triviality Result for Semilinear Parabolic Equations, Math. Engineering 4, 2022.

Carlo Mantegazza and Marco Pozzetta
The Lojasiewicz-Simon Inequality for the Elastic Flow, Calc. Var. 60, 2021.

Carlo Mantegazza, Alessandra Pluda and Marco Pozzetta
A Survey of the Elastic Flow of Curves and Networks, Milan J. Math. 89, 59-121, 2021.

Carlo Mantegazza
Some Elementary Questions in the Calculus of Variations, Rend. Semin. Mat. Univ. Padova 145, 107-115, 2021.

Daniele Castorina and Carlo Mantegazza
Ancient Solutions of Superlinear Heat Equations on Riemannian Manifolds, Communications in Contemp. Math. 23, 2050033 (16 pages), 2021.

Daniele Castorina, Carlo Mantegazza and Berardino Sciunzi
A Liouville Theorem for Superlinear Heat Equations on Riemannian Manifolds, Milan J. Math. 87, 303-313, 2019.

Pietro Baldi, Emanuele Haus and Carlo Mantegazza
Existence of a Lens-Shaped Cluster of Surfaces Self-Shrinking by Mean Curvature, Math. Ann. 375, 1857-1881, 2019.

Carlo Mantegazza, Matteo Novaga and Alessandra Pluda
Lectures on Curvature Flow of Networks, Contemporary Research in Elliptic PDEs and Related Topics, Springer INdAM Series 33, 369-417, 2019.

Pietro Baldi, Emanuele Haus and Carlo Mantegazza
Non-Existence of Theta-Shaped Self-Similarly Shrinking Networks Moving by Curvature, Communications in PDE 43, 403-427, 2018.

Riccardo Benedetti and Carlo Mantegazza
La Congettura di Poincaré e il Flusso di Ricci, Rivista dell'UMI - Matematica, Cultura e Società 2, 245-289, 2017.

Pietro Baldi, Emanuele Haus and Carlo Mantegazza
On the Classification of Networks Self-Similarly Moving by Curvature, Geom. Flows 2, 125-137, 2017.

Carlo Mantegazza, Samuele Mongodi and Michele Rimoldi
The Cotton Tensor and the Ricci Flow, Geom. Flows 2, 49-71, 2017.

Pietro Baldi, Emanuele Haus and Carlo Mantegazza
Networks Self-Similarly Moving by Curvature with Two Triple Junctions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28, 323-338, 2017.

Giovanni Catino, Laura Cremaschi, Zindine Djadli, Carlo Mantegazza and Lorenzo Mazzieri
The Ricci-Bourguignon Flow, Pacific J. Math. 287, 337-370, 2017.

Daniele Castorina and Carlo Mantegazza
Ancient Solutions of Semilinear Heat Equations on Riemannian Manifolds, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28, 85-101, 2017.

Carlo Mantegazza, Matteo Novaga and Alessandra Pluda
Motion by Curvature of Networks with Two Triple Junctions, Geom. Flows 2, 18-48, 2016.

Riccardo Benedetti and Carlo Mantegazza (editors)
Ricci Flow and Geometric Applications - CIME Summer School in Cetraro, June 28 - July 3 2010, Lecture Notes in Mathematics/CIME Foundation Subseries 2166, Springer, 2016.

Annibale Magni, Carlo Mantegazza and Matteo Novaga
Motion by Curvature of Planar Networks II, Annali Sc. Norm. Super. Pisa CL. Sci. 15, 117-144, 2016.

Carlo Mantegazza and Reto Müller
Perelman's Entropy Functional at Type I Singularities of the Ricci Flow, J. Reine Angew. Math. (Crelle's Journal) 703, 173-199, 2015.

Laura Cremaschi and Carlo Mantegazza
Short-Time Existence of the Second Order Renormalization Group Flow in Dimension Three, Discrete Contin. Dyn. Syst. - Series A 35, 5787-5798, 2015.

Giovani Catino, Carlo Mantegazza and Lorenzo Mazzieri
Locally Conformally Flat Ancient Ricci Flows, Analysis & PDE 8, 365-371, 2015.

Giovanni Catino, Carlo Mantegazza and Lorenzo Mazzieri
A Note on Codazzi Tensors, Math. Ann. 362, 629-638, 2015.

Carlo Mantegazza, Giovanni Mascellani and Gennady Uraltsev
On the Distributional Hessian of the Distance Function, Pacific. J. of Math. 270, 151-166, 2014.

Annibale Magni, Carlo Mantegazza
A Note on Grayson's Theorem, Rend. Semin. Mat. Univ. Padova 131, 263-279, 2014.

Nicola Gigli and Carlo Mantegazza
A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport, Advances in Math. 250, 74-104, 2014.

Huai-Dong Cao, Giovanni Catino, Qiang Chen, Carlo Mantegazza and Lorenzo Mazzieri
Bach-Flat Gradient Steady Ricci Solitons, Calc. Var. 49, 125-138, 2014.

Annibale Magni, Carlo Mantegazza and Efstratios Tsatis
Flow by Mean Curvature inside a Moving Ambient Space, J. Evol. Eqs. 13, 561-576, 2013.

Giovanni Catino, Carlo Mantegazza, Lorenzo Mazzieri and Michele Rimoldi
Locally Conformally Flat Quasi-Einstein Manifolds, J. Reine Angew. Math. (Crelle's Journal) 675, 181-189, 2013.

Giovanni Catino, Carlo Mantegazza and Lorenzo Mazzieri
On the Global Structure of Conformal Gradient Solitons with Nonnegative Ricci Tensor, Communications in Contemp. Math. 14, 1250045, 12 pp., 2012.

Carlo Mantegazza and Luca Martinazzi
A Note on Quasilinear Parabolic Equations on Manifolds, Annali Sc. Norm. Super. Pisa CL. Sci. 11, 857-874, 2012.

Carlo Mantegazza
Lecture Notes on Mean Curvature Flow, Birkhäuser Verlag, 2011.
Errata of the Book - 27/3/2013

Giovanni Catino and Carlo Mantegazza
Evolution of the Weyl Tensor under the Ricci Flow, Ann. Inst. Fourier 61, 1407-1435, 2011.

Marco Caldarelli, Giovanni Catino, Zindine Djadli, Annibale Magni and Carlo Mantegazza
On Perelman's Dilaton, Geom. Dedicata 145, 127-137, 2010.

Annibale Magni and Carlo Mantegazza
Some Remarks on Huisken's Monotonicity Formula for Mean Curvature Flow, in Singularities in Nonlinear Evolution Phenomena and Applications (M. Novaga and G. Orlandi eds.), CRM Series of Center "Ennio De Giorgi", Pisa, 157-169, 2009.

Manolo Eminenti, Gabriele La Nave and Carlo Mantegazza
Ricci Solitons - The Equation Point of View, Manuscripta Math. 127, 345-367, 2008.

Giovanni Bellettini, Carlo Mantegazza and Matteo Novaga
Singular Perturbations of Mean Curvature Flow, J. Diff. Geom. 75, 403-431, 2007.

Carlo Mantegazza
Evolution by Curvature of Networks of Curves in the Plane, Progress in Nonlin. Diff. Eqs. and Appl. 59, 95-109, 2004.

Manolo Eminenti and Carlo Mantegazza
Some Properties of the Distance Function and a Conjecture of De Giorgi, J. Geom. Anal. 14, 267-279, 2004.

Carlo Mantegazza, Matteo Novaga and Vincenzo Maria Tortorelli
Motion by Curvature of Planar Networks, Annali Sc. Norm. Super. Pisa Cl. Sci. 3, 235-324, 2004.

Carlo Mantegazza and Andrea Carlo Mennucci
Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds, Appl. Math. Opt. 47, 1-25, 2003.

Carlo Mantegazza
Smooth Geometric Evolutions of Hypersurfaces, Geom. and Funct. Anal. 12, 138-182, 2002.

Irene Fonseca and Carlo Mantegazza
Second Order Singular Perturbation Models for Phase Transitions, SIAM J. Math. Anal. 31, 1121-1143, 2000.

Luigi Ambrosio, Camillo De Lellis and Carlo Mantegazza
Line Energies for Gradient Vector Fields in the Plane, Calc. Var. 9, 327-355, 1999.

Ilaria Fragalà and Carlo Mantegazza
On some Notions of Tangent Space to a Measure, Proc. Roy. Soc. Edinburgh Sect. A 129A, 331-342, 1999.

Luigi Ambrosio and Carlo Mantegazza
Curvature and Distance Function from a Manifold, J. Geom. Anal. 8, 723-748, 1998.

Giovanni Alberti and Carlo Mantegazza
A Note on the Theory of SBV Functions, BUMI 11-B, 375-382, 1997.

Carlo Mantegazza
Curvature Varifolds with Boundary, J. Diff. Geom. 43, 807-843, 1996.

Degree Thesis Su Alcune Definizioni Deboli di Curvatura per Insiemi Non Orientati Math. Dept. University of Pisa, 1993 - Advisor: Luigi Ambrosio Perfezionamento - PhD Thesis Smooth Geometric Evolutions of Hypersurfaces and Singular Approximation of Mean Curvature Flow Scuola Normale Superiore di Pisa, 2014 - Advisor: Luigi Ambrosio

Unpublished Notes

Varifold con Seconda Forma Fondamentale e Bordo, 1994.
The Chebyshev Problem, 1997.
Universal Interpolation Inequalities, 2002.
Curves Homothetically Shrinking by Curvature, 2009 (with Annibale Magni).
Star-Shapedness under Mean Curvature Flow, 2010.
Notes on the Distance Function from a Submanifold, Lecture Notes, 2010.
Locally Conformally Flat Warped Manifolds, 2012.
Some Entropies for Mean Curvature Flow, 2013.
On the Minimality of the Potential Function of a Gradient Shrinking Ricci Soliton, 2016.
On C² Umbilical Hypersurfaces, 2021.
A Note on the Lalescu Sequence, 2024.

Esercizi dal Corso "Complementi di Matematica" I Anno SNS 2013/14 - Soluzioni
Esercizi di Teoria della Misura
Problemi di Analisi I dal Corso del I Anno alla Scuola Normale Superiore di Pisa, Amazon, 2016.
Appunti di Calcolo delle Variazioni, Amazon, 2019.
Quesiti a Risposta Multipla di Analisi Matematica 1, Esculapio, 2020.
Complementi di Matematica, Edizioni della Normale, 2021.

Erich Monteleone - Il Problema di Chebyshev, Degree Side-Thesis, Math. Dept. Univ. Pisa, 2000.
Giovanni Catino - Some Integral Pinching Results in Riemannian Geometry, PhD Thesis, Math. Dept. Univ. Pisa, 2009.
Annibale Magni - Some Results in Geometric Evolution Problems, PhD Thesis, SISSA Trieste, 2009.
Giovanni Mascellani - Fourth-Order Geometric Flows and Integral Pinching of the Curvature, Master Thesis, SNS Pisa, 2013.
Laura Cremaschi - Some Variations on Ricci Flow, PhD Thesis, SNS Pisa, 2016.
Alessandra Pluda (with Matteo Novaga) - Minimal and Evolving Networks, PhD Thesis, Math. Dept. Univ. Pisa, 2016.
Francesca Oronzio (with Virginia Agostiniani)
   - Alcune Relazioni tra Curvatura e Topologia per mezzo delle Funzioni Distanza, Master Thesis, Math. Dept. Univ. Napoli Federico II, 2018.
   - ADM Mass and Linear Potential Theory, PhD Thesis, Math. Dept. Univ. Napoli Federico II, 2022.
Serena Della Corte - Long-time Behavior Results for the Modified Mullins-Sekerka Flow, Master Thesis, Math. Dept. Univ. Napoli Federico II, 2020.
Antonia Diana
   - Nonlinear Stability for the Surface Diffusion Flow, Master Thesis, Math. Dept. Univ. Napoli Federico II, 2020.
   - The Surface Diffusion Flow. Long-Time Behavior and Asymptotic Stability, PhD Thesis, Scuola Superiore Meridionale, Napoli, 2024.
Luigi Marigliano - The Weyl Tensor of Riemannian Manifolds and some Topological Invariants in Dimension Four, Master Thesis, Math. Dept. Univ. Napoli Federico II, 2023.
Aurora Corbisiero - La Formula di Santaló, Degree Thesis, Math. Dept. Univ. Napoli Federico II, 2023.

Evoluzioni di Strutture Geometriche - PhD Day, Napoli, 2015.
Perelman, il Flusso di Ricci e la Congettura di Poincaré - Happy Numbers, Camerino 2016.
Perelman, the Ricci Flow and the Poincaré Conjecture - Pisa 2016.
Corso di Analisi Matematica - Ennio De Giorgi, SNS 1991/1992 - Note di Vincenzo Maria Tortorelli (a cura di Carlo Mantegazza e Vincenzo Maria Tortorelli, con un'appendice di Luigi Ambrosio), Quaderni dell'Accademia Pontaniana 63, Napoli, 2016.
Evolution of planar networks of curves with multiple junctions (video) - Pisa 2017 (with Alessandra Pluda).
Motion by curvature of networks in the plane (video) - ICTP, Trieste 2018.
Matematica (quasi) senza numeri (video) - Corso di orientamento SNS per studenti delle scuole superiori, Napoli, 2019.
Matematica (quasi) senza numeri - Campus MFS, Bardonecchia, 2020.
Perelman, il Flusso di Ricci e la Congettura di Poincaré (video) - Seminari del Centenario UMI (locandina), Napoli, 2022.
Matematica (quasi) senza numeri - Prisma 46, 2022 (con Silvia Benvenuti).
Matematica (quasi) senza numeri (video) - IV Congresso Nazionale della Federazione Italiana Mathesis, Napoli, 2022.
La congettura di Poincaré - Nuova Lettera Matematica, 2024.
Un solo giorno di gioia ne vale la pena - Il teorema di Margherita - Prisma 63, 2024.

Relazione Buratti - Campionato Europeo di Bridge 2005 (con Manolo Eminenti).
Intervista Repubblica - 28/2/2013.

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