Geodesic
Alessio Figalli's contributionsto nonlocal minimal surfaces
Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 119-124.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Alessio has produced in his very intense career an extraordinary number of outstanding results in an impressive variety of topics. Among the multifold research lines in which he acted as a trailblazer, the one focused on nonlocal minimal surfaces offered an excellent opportunity for Alessio to pioneer some of the first settlements in a brand new subject of investigation and pave the way to a broad spectrum of future research.
Nella sua intensa carriera, Alessio ha prodotto un numero straordinario di risultati eccezionali riguardanti una varietà impressionante di temi di ricerca. Tra le molteplici direzioni intraprese, quella riguardante le superfici minime nonlocali ha proposto Alessio come un leader mondiale per i suoi contributi stimolanti e innovativi. 
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Dipierro, Serena; Valdinoci, Enrico. Alessio Figalli's contributionsto nonlocal minimal surfaces. Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 119-124. http://geodesic.mathdoc.fr/item/RUMI_2019_1_4_2_a6/

[BFV14] Begoña Barrios, Alessio Figalli, and Enrico Valdinoci, Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), no. 3, 609-639. MR3331523 | MR | Zbl

[CRS10] L. Caffarelli, J.-M. Roquejoffre, and O. Savin, Nonlocal minimal surfaces, Comm. Pure Appl. Math. 63 (2010), no. 9, 1111-1144, DOI 10.1002/cpa.20331. MR2675483 | DOI | MR | Zbl

[CFMN18] Giulio Ciraolo, Alessio Figalli, Francesco Maggi, and Matteo Novaga, Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature, J. Reine Angew. Math. 741 (2018), 275-294, DOI 10.1515/crelle-2015-0088. MR3836150 | DOI | MR | Zbl

[CF17] Matteo Cozzi and Alessio Figalli, Regularity theory for local and nonlocal minimal surfaces: an overview, Nonlocal and nonlinear di usions and interactions: new methods and directions, Lecture Notes in Math., vol. 2186, Springer, Cham, 2017, pp. 117-158. MR3588123 | MR | Zbl

[DFPV13] Serena Dipierro, Alessio Figalli, Giampiero Palatucci, and Enrico Valdinoci, Asymptotics of the s-perimeter as $s \searrow 0$, Discrete Contin. Dyn. Syst. 33 (2013), no. 7, 2777-2790, DOI 10.3934/dcds.2013.33.2777. MR3007726 | DOI | MR | Zbl

[FFM+ 15] A. Figalli, N. Fusco, F. Maggi, V. Millot, and M. Morini, Isoperimetry and stability properties of balls with respect to nonlocal energies, Comm. Math. Phys. 336 (2015), no. 1, 441-507, DOI 10.1007/s00220-014-2244-1. MR3322379 | DOI | MR | Zbl

[FV17] Alessio Figalli and Enrico Valdinoci, Regularity and Bernstein-type results for nonlocal minimal surfaces, J. Reine Angew. Math. 729 (2017), 263-273, DOI 10.1515/crelle-20150006. MR3680376 | DOI | MR | Zbl