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Francesco Maggi

Department of Mathematics

Calculus of Variations and Geometric Measure Theory


Phone: 512-471-5139

Office Location
PMA 10.124

Postal Address
AUSTIN, TX 78712

Full professor UT Austin, USA, 2016/present

Member Institute for Advanced Study, Princeton, USA, Spring 2019

Research scientist ICTP Trieste, Italy, 2016/2017 

Associate professor UT Austin, USA, 2012/2015

Professore associato (Associate prof.), U. Firenze, Italy, 2011/2012

(Assistant prof.), U. Firenze, Italy, 2005/2011

Wissenschaftlichen Assistenten C1 
(Assistant prof.) U. Duisburg-Essen, Germany, 2005

Postdoctoral associate, MPI-MIS Leipzig, Germany, 2004

Ph.D. in Mathematics
, U. Firenze, Italy, 2004

Visiting graduate student 
MPI-MIS Leipzig, Germany, Fall 2002 and Fall 2003

Visiting graduate student Carnegie Mellon University, Pittsburgh, USA, Spring 2003

M.S. in Mathematics
, U. Firenze, Italy, 2000

55 Maggi, Francesco; Scardicchio, Antonello; Stuvard, Salvatore. Soap films with gravity and almost-minimal surfaces, Preprint arXiv:1807.05200

54 Delgadino, Matias; Maggi, Francesco. Alexandrov's theorem revisited, Preprint arXiv:1711.07690

53 Cavalletti, Fabio; Maggi, Francesco; Mondino, Andrea. Quantitative isoperimetry à la Lévy-Gromov. Accepted on Comm. Pure Appl. Math.Preprint arXiv:1707.04326

52 Delgadino, Matias; Maggi, Francesco; Mihaila, Cornelia; Neumayer, Robin, Bubbling with L2 almost constant mean curvature and an Alexandrov-type theorem for crystals. Accepted on Archive for Rational Mechanics and Analysis. Preprint arXiv:1705.10117

51 Cavalletti, Fabio; Maggi, Francesco; Mondino, Andrea. Rigidity for critical points in the Lévy-Gromov inequality. Accepted on Mathematische Zeitschrift.  Preprint arXiv:1612.04119

50 Figalli, Alessio; Maggi, Francesco; Mooney, Connor. The sharp quantitative Euclidean concentration inequality. Accepted on Cambridge Journal of Mathematics.Preprint arXiv:1601.04100v2

49 Dipierro, Serena; Maggi, Francesco; Valdinoci, Enrico. Asymptotic expansions of the contact angle in nonlocal capillarity problems. Accepted on Journal of Nonlinear Science.PreprintarXiv:1610.00075

48 Maggi, Francesco; Valdinoci, Enrico. Capillarity problems with nonlocal surface tension energies. Accepted on Comm. PDE.Preprint arXiv:1606.08610

47 Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco. A quantitative analysis of metrics in R^n with almost constant positive scalar curvature, with applications to fast diffusion flows. Accepted on Int. Math. Res. Not. IMRNPreprint arXiv:1602.01916

46 Cicalese, Marco; Leonardi, Gian Paolo; Maggi, Francesco. Sharp stability inequalities for planar double bubbles. Accepted on Interfaces Free Bound.Preprint arXiv:1211.3698

45 Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco; Novaga, Matteo. Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. Accepted on Journal für die reine und angewandte Mathematik(Crelle's Journal).Preprint arXiv:1503.00653

44 Carlen, Eric; Maggi, Francesco. Stability for the Brunn-Minkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range non-local isoperimetry. (2017) Canad. J. Math. 69, 1036-1063. Preprint arXiv:1507.03454.

43 Maggi, Francesco; Neumayer, Robin. A bridge between Sobolev and Escobar inequalities and beyond (2017) J. Funct. Anal. 273(6),2070-2106. Preprint arXiv:1609.02346

42 Krummel, Brian; Maggi, Francesco. Isoperimetry with upper mean curvature bounds and sharp stability estimates (2017) Calc. Var. PDE. 56(2), Paper no. 53, 43 pp.Preprint arXiv:1606.00490

41 Ciraolo, Giulio; Maggi, Francesco. On the shape of compact hypersurfaces with almost constant mean curvature (2017) Comm. Pure Appl. Math. 70(4), 665-716.Preprint arXiv:1503.06674

40 Colombo, Maria; Maggi, Francesco. Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters (2017) Nonlinear Anal. 153, 243-274.Preprint arXiv:1605.05641

39 Leonardi, Gian Paolo; Maggi, Francesco (2017)  Improved convergence theorems for bubble clusters. II. The three-dimensional case. Indiana Univ. Math. J. 66(2), 559-608. Preprint arXiv:1505.06709.

38 De Lellis, Camillo; Ghiraldin, Francesco; Maggi, Francesco (2017) A direct approach to Plateau's problem. J. Eur. Math. Soc. (JEMS) 19(8), 2219-2240.Preprint arXiv:1408.4047

37 Cagnetti, Filippo; Colombo, Maria; De Philippis, Guido; Maggi Francesco (2017) Essential connectedness and the rigidity problem for Gaussian symmetrization. J. Eur. Math. Soc. (JEMS) 19(2) 395-439.Preprint arXiv:1304.4527

36 De Philippis, Guido; Maggi, Francesco (2017). Dimensional estimates for singular sets in geometric variational problems with free boundaries.J. Reine Angew. Math.(Crelle's Journal), 725, 217-234.Preprint arXiv:1407.4834

35 Maggi, Francesco; Mihaila, Cornelia. On the shape of capillarity droplets in a container (2016) Calc. Var. PDE. 55(5), Paper no. 122, 42 pp. Preprint arXiv:1509.03324

34 Cicalese, Marco; Leonardi, Gian Paolo; Maggi, Francesco. (2016) Improved convergence theorems for bubble clusters. I. The planar case. Indiana Univ. Math. J. 65(6), 1979-2050.Preprint arXiv:1409.6652.

33 Caroccia, Marco; Maggi, Francesco. (2016)A sharp quantitative version of Hales' isoperimetric honeycomb theorem, J. Math. Pures Appl. (9) 106(5), 935-956. Preprint arXiv:1410.6128.

32 Figalli, Alessio; Fusco, Nicola; Maggi, Francesco; Millot, Vincent; Morini, Massimiliano (2015). Isoperimetry and stability properties of balls with respect to nonlocal energies. Comm. Math. Phys. 336(1), 441-507. Preprint arXiv:1403.0516

31 De Philippis, Guido; Maggi, Francesco (2015). Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law. Arch. Ration. Mech. Anal. 216(2), 473-568. Preprint arXiv:1402.0549

30 Cagnetti, Filippo; Colombo, Maria; De Philippis, Guido; Maggi Francesco (2014). Rigidity of equality cases in Steiner's perimeter inequality. Anal. PDE, 7(7), 1535-1593. Preprint arXiv:1309.1639

29 De Philippis, Guido; Maggi, Francesco (2014). Sharp stability inequalities for the Plateau problem. J. Differential Geom. 96(3), 399-456.

28 Maggi, Francesco; Ponsiglione, Marcello; Pratelli, Aldo (2014) Quantitative stability in the isodiametric inequality via the isoperimetric inequality. Trans. AMS 366(3), 1141-1160.

27 Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo (2014). A geometric approach to correlation inequalities in the plane. Ann. Inst. Henri Poincaré Probab. Stat. 50(1), 1-14.

26 Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo (2013). Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation, Adv. Math. 242, 80-101. 

25Figalli, Alessio; Maggi, Francesco (2013) On the isoperimetric problem for radial log-convex densities, Calc. Var. Partial Differential Equations 48(3-4), 447-489. 

24 Figalli, Alessio; Maggi, Francesco; (2011) On the shape of liquid drops and crystals in the small mass regime. Arch. Ration. Mech. Anal. 201(1), 143-207.

23 Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (2011). On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density. J. Funct. Anal. 260(12), 3678-3717. 

22 Cianchi, Andrea; Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (2011) On the isoperimetric deficit in Gauss space. Amer. J. Math. 133(1), 131-186. 

21 Fonseca, Irene; Leoni, Giovanni; Maggi, Francesco; Morini, Massimiliano (2010) Exact reconstruction of color images by a total variation model, Ann. Inst. H. Poincaré Anal. Non Linéaire 27,1291-1331.

20 Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo (2010). A mass transportation approach to quantitative isoperimetric inequalities, Invent. Math. 182, 167-211. 

19 Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo (2009). A refined Brunn-Minkowski inequality for convex sets, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26, 2511-2519. 

18 Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo (2009). A note on Cheeger sets, Proc. AMS 137(6), 2057–2062. 

17 Cianchi, Andrea; Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (2009), The sharp Sobolev inequality in quantitative form, J. Eur. Math. Soc. (5),1105–1139. 

16 Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (2009) Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 51–71. 

15 Maggi, Francesco (2008). Some methods for studying stability in isoperimetric type problems, Bull. AMS 45(3), 367-408. 

14 Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (2008). The sharp quantitative isoperimetric inequality, Ann. of Math. (2) 168(3),941-980. 

13 Maggi, Francesco; Villani, Cédric (2008). Balls have the worst best Sobolev inequalities. Part two: variants and extensions, Calc. Var. PDE 31(1), 47-74. 

12 Conti, Sergio; Maggi, Francesco, (2008). Confining thin elastic sheets and folding paper.Arch. Ration. Mech. Anal. 187(1), 1-48. 

11 Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (2007) The sharp quantitative Sobolev inequality for functions of bounded variation J. Funct. Anal. 244(1)315-341. 

10 Conti, Sergio; Maggi, Francesco; Müller, Stefan (2006) Rigorous derivation of Föppl’s theory for clamped elastic membranes leads to relaxation, SIAM J. Math. Anal. 38(2) 657-680. 

Fusco, Nicola; Gori, Michele; Maggi, Francesco (2006). A remark on Serrin’s theorem. NoDEA 13(4),425-433. 

Conti, Sergio; Faraco, Daniel; Maggi, Francesco; Müller, Stefan (2005). Rank-one convex functions on 2 × 2 symmetric matrices and laminates on rank-three lines. Calc. Var. PDE 24(4), 479-493. 

Conti, Sergio; Faraco, Daniel; Maggi, Francesco (2005) A new approach to counterexamples to L1estimates: Korn’s inequality, geometric rigidity and regularity for gradients of separately convex functions, Arch. Ration. Mech. Anal. 175(2), 287-300. 

Gori, Michele; Maggi, Francesco (2005). The common root of the geometric conditions in Serrin’s lower semicontinuity theorem.Ann. Mat. Pura e Applicata,184(1), 95-114. 

Maggi, Francesco; Villani, Cédric (2005). Balls have the worst best Sobolev inequalities. J. Geom. Anal. 15(1), 83-121. 

Maggi, Francesco; Morini, Massimiliano (2004). A Γ-convergence result for variational integrators of quadratic lagrangians.ESAIM: COCV 10(4), 656-665.

Maggi, Francesco (2003) On the relaxation on BV of certain non-coercive integral functionals, J. Convex Anal. 10(2), 477-489. 

Gori, Michele; Maggi, Francesco (2003) On the lower semicontinuity of supremal functionals, ESAIM: COCV 9, 135-143.

Gori, Michele; Maggi, Francesco; Marcellini, Paolo (2003). On some sharp conditions for lower semicontinuity in L1. Diff. Int. Equations 16(1),51-76.

Books and lecture notes:

Maggi, Francesco (2012). Sets of finite perimeter and geometric variational problems: an introduction to Geometric Measure Theory,Cambridge Studies in Advances Mathematics 135, Cambridge University Press, 2012.

Maggi, Francesco (2008).Symmetrization, optimal transport and quantitative isoperimetric inequalities. This is a chapter in: Optimal transportation, Geometry and Functional inequalities (Edited by Luigi Ambrosio). Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series, 11. Edizioni della Normale, Pisa, 2010.