Alessio Figalli's contributionsto nonlocal minimal surfaces

Serena Dipierro; Enrico Valdinoci

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana (2019)

  • Volume: 4, Issue: 2, page 119-124
  • ISSN: 2499-751X

Abstract

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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.

How to cite

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Dipierro, Serena, and Valdinoci, Enrico. "Alessio Figalli's contributionsto nonlocal minimal surfaces." Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana 4.2 (2019): 119-124. <http://eudml.org/doc/295097>.

@article{Dipierro2019,
abstract = {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.},
author = {Dipierro, Serena, Valdinoci, Enrico},
journal = {Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana},
language = {eng},
month = {8},
number = {2},
pages = {119-124},
publisher = {Unione Matematica Italiana},
title = {Alessio Figalli's contributionsto nonlocal minimal surfaces},
url = {http://eudml.org/doc/295097},
volume = {4},
year = {2019},
}

TY - JOUR
AU - Dipierro, Serena
AU - Valdinoci, Enrico
TI - Alessio Figalli's contributionsto nonlocal minimal surfaces
JO - Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
DA - 2019/8//
PB - Unione Matematica Italiana
VL - 4
IS - 2
SP - 119
EP - 124
AB - 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.
LA - eng
UR - http://eudml.org/doc/295097
ER -

References

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  1. BARRIOS, BEGOÑA, FIGALLI, ALESSIO, and VALDINOCI, ENRICO, 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 Zbl1316.35061MR3331523
  2. CAFFARELLI, L., ROQUEJOFFRE, J.-M., and SAVIN, O., Nonlocal minimal surfaces, Comm. Pure Appl. Math.63 (2010), no. 9, 1111-1144, DOI 10.1002/cpa.20331. MR2675483 Zbl1248.53009MR2675483DOI10.1002/cpa.20331
  3. CIRAOLO, GIULIO, FIGALLI, ALESSIO, MAGGI, FRANCESCO, and NOVAGA, MATTEO, 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 Zbl1411.53030MR3836150DOI10.1515/crelle-2015-0088
  4. COZZI, MATTEO and FIGALLI, ALESSIO, 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 Zbl1385.49028MR3588123
  5. DIPIERRO, SERENA, FIGALLI, ALESSIO, PALATUCCI, GIAMPIERO, and VALDINOCI, ENRICO, Asymptotics of the s-perimeter as s ↘ 0 , Discrete Contin. Dyn. Syst.33 (2013), no. 7, 2777-2790, DOI 10.3934/dcds.2013.33.2777. MR3007726 Zbl1275.49083MR3007726DOI10.3934/dcds.2013.33.2777
  6. FIGALLI, A., FUSCO, N., MAGGI, F., MILLOT, V., and MORINI, M., 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 Zbl1312.49051MR3322379DOI10.1007/s00220-014-2244-1
  7. FIGALLI, ALESSIO and VALDINOCI, ENRICO, Regularity and Bernstein-type results for nonlocal minimal surfaces, J. Reine Angew. Math.729 (2017), 263-273, DOI 10.1515/crelle-20150006. MR3680376 Zbl1380.49060MR3680376DOI10.1515/crelle-2015-0006

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