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Publications

To open a preprint\postprint version of the articles, click on the title; for the published version click on the DOI.

Coaserning  phenomena in the network flow

with Yoshihiro Tonegawa

Bruno Pini Mathematical Analysis seminar 2024

Lojasiewicz-Simon inequalities for minimal networks: stability and convergence,

with Marco Pozzetta,

Math. Ann. (2023) 

DOI: 10.1007/s00208-023-02714-7

Minimizing properties of networks via local and global calibrations

with Marco Pozzetta,

Bull. Lond. Math. Soc., 2023, 55(6), pp. 3029–3052

DOI: 10.1112/blms.12908

Evolution of networks with multiple junctions,

with Carlo Mantegazza, Matteo Novaga, and Felix Schulze

accepted: Astérisque

Type-0 singularities in the network flow - Evolution of trees,

with Carlo Mantegazza and Matteo Novaga,

J. Reine Angew. Math., vol. 2022, no.792, pp.189-221 (2022)

DOI: 10.1515/crelle-2022-0055

Short-time existence for the network flow,
with Jorge Lira, Rafe Mazzeo and Mariel Saez,

Comm. Pure Appl. Math., 2023, 76(12), pp. 3968–4021

DOI: 10.1002/cpa.22111                                                  

Existence and uniqueness of the Motion by Curvature of regular networks,

with Michael Gößwein and Julia Menzel,

Interfaces Free Bound. 2023, 25(1), pp. 109-154

DOI: 10.4171/IFB/477

Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves,

with Christopher Brand and Georg Dolzmann,

ZAMM  Z. Angew. Math. Mech. (2021)

DOI: 10.1002/zamm.202100169

A survey of the Elastic Flow of curves and networks,

with Carlo Mantegazza and Marco Pozzetta,

Milan J. Math. (2021)

DOI: 10.1007/s00032-021-00327-w

Degenerate elastic networks,

with Giacomo Del Nin and Marco Pozzetta,

J. Geom. Anal., 31, pages 6128–6170 (2021)

DOI: 10.1007/s12220-020-00521-z

The oriented mailing problem and its convex relaxation,

with Marcello Carioni, Andrea Marchese, Annalisa Massaccesi, Riccardo Tione,

Nonlinear Anal. 199 (2020), no.112035

DOI: 10.1016/j.na.2020.112035

Long time existence of solutions to an Elastic Flow of networks,

with Harald Garcke and Julia Menzel,

Comm. Partial Differential Equations, 2020, 45(10), pp. 1253-1305.

DOI: 10.1080/03605302.2020.1771364                                                                

On different notions of calibrations for minimal partitions and minimal networks in R^2, with Marcello Carioni,

Adv. Calc. Var., vol. 14, no. 3, 2021, pp. 401-417.

DOI: 10.1515/acv-2019-0005                                   

Willmore flow of planar networks, 

with Harald Garcke, Julia Menzel,

J. Differential Equations, 266 (2019), no.4, 2019-2051

DOI: 10.1016/j.jde.2018.08.019                                                       

Minimal elastic networks, 

with Anna Dall'Acqua, Matteo Novaga,

Indiana Univ. Math. J.  69 (2020), no.6, 1909-1932

DOI: 10.1512/iumj.2020.69.8036                                                       

Lecture on curvature flow of networks,

with Carlo Mantegazza and Matteo Novaga,

in ``Contemporary Research in Elliptic PDEs and Related Topics", Springer INDAM series 33, (2019).

DOI: 10.1007/978-3-030-18921-1                                                                                      

Some minimization problems for planar networks of elastic curves,

with Anna Dall'Acqua,

Geom. Flows, 3 (2017), pp. 105-124.

DOI: 10.1515/geofl- 2017- 0005                                                                         

Spines of minimal length,

with Bruno Martelli, Matteo Novaga, and Stefano Riolo,

Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVII (2017) Issue 3, 1067-1090

DOI: 10.2422/2036-2145.201511_003                         

Nontrivial solutions of quasilinear elliptic equations with natural growth conditions,

with Marco Degiovanni,

in ``Solvability, Regularity, Optimal Control of Boundary Value Problems for PDEs'', Springer INDAM series 22, (2017), 183-198.

DOI: 10.1007/978-3-319-64489-9 

Motion by curvature of networks with two triple junctions,

with Carlo Mantegazza and Matteo Novaga,

Geom. Flows, 2 (2016), 18-48.

DOI: 10.1515/geofl-2016-0002                                                                                          

Evolution of spoon-shaped networks,

Netw. Heterog. Media,11 (2016) n.3, 509-526.

DOI: 10.3934/nhm.2016007                                       

Preprints

​On the uniqueness of nondegenerate blowups for the motion by curvature of networks

with Marco Pozzetta (April 2022). ​

​A note on Ricci-pinched 3-manifolds

with Luca Benatti, Francesca Oronzio, and Carlo Mantegazza (September 2024).

Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas

with Luca Benatti, and Marco Pozzetta (November 2024).

​​

Proceedings

Coaserning  in the network flow

(Oberwolfach report No. 07/2024 "Interfaces, Free Boundaries and Geometric Partial Differential Equations");

Network flow: resolution of singularites and stability                                                 (Oberwolfach report No. 37/2022 "Calculus of Variations");

Elastic networks, statics and dynamics, 

with Matteo Novaga (11th Mathematical Society of Japan (MSJ) Seasonal Institute (SI));

Calibrations in families for minimal networks,   

with Marcello Carioni (89th GAMM annual meeting);

Willmore flow of planar networks, 

with Harald Garcke, Julia Menzel (89th GAMM annual meeting);

​​

Thesis

  • Minimal and evolving networks  

    Ph.D. thesis      

    11 November 2016, Università di Pisa;

  • Teoria del grado per operatori multivoci

    Master thesis

    15 July 2013, Università Cattolica del Sacro Cuore, Brescia;

  • Disuguaglianza isodiametrica

    Bachelor thesis

    8 July 2011, Università Cattolica del Sacro Cuore, Brescia.

 

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