Carlo Mantegazza
Mathematical Analysis
Dipartimento di Matematica e
Applicazioni "Renato Caccioppoli"
Email: carlo.mantegazza@unina.it |
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)
Curriculum
Current Research
Calculus of variations and geometric measure theory
Functionals depending on curvature
Geometric evolutions
Nonlinear problems in Riemannian geometry |
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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
Smooth Geometric Evolutions of Hypersurfaces and Singular Approximation of Mean Curvature Flow |
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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 - 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.
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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