F. Maggi:
On the relaxation on $BV$ of certain non coercive integral functionals
J. Convex Anal. Vol. 10, N. 2, p. 477-489, 2003

N. Fusco, M. Gori, F. Maggi:
A remark on Serrin's Theorem
Nonlinear Differential Equations and Applications (Accepted Paper) 2003

M. Gori, F. Maggi, P. Marcellini:
On some sharp conditions for lower semicontinuity in $L^1$
Differential and Integral Equations Vol. 16, p. 51-76, 2003

M. Gori, F. Maggi:
On the Lower Semicontinuity of Supremal Functionals
ESAIM: COCV Vol. 9, p. 135-143, 2003

F. Maggi:
On Serrin's Lower Semicontinuity Problem
(Ph.D. Thesis) p. 103, 2004

S. Conti, D. Faraco, F. Maggi:
A new approach to counterexamples to $L^1$ estimates: Korn's inequality, geometric rigidity and regularity for gradients of separately convex functions
Arch. Ration. Mech. Anal. Vol. 175, N. 2, p. 287-300, 2005

F. Maggi, C. Villani:
Balls Have the Worst Best Sobolev Inequalities
J. Geom. Anal. Vol. 15, N. 1, p. 83-121, 2005

S. Conti, D. Faraco, F. Maggi, S. Müller:
Rank-one convex functions on 2x2 symmetric matrices and laminates on rank-three lines
Calc. Var. Partial Differential Equations Vol. 24 , N. 4, p. 479-493, 2005

M. Gori, F. Maggi:
The common root of the geometric conditions in Serrin's lower semicontinuity theorem
Ann. Mat. Pura Appl. (4) Vol. 184, N. 1, p. 95-114, 2005

S. Conti, F. Maggi:
Confining thin elastic sheets and folding paper
Archive for Rational Mechanics and Analysis (Accepted Paper) 2005

N. Fusco, F. Maggi, A. Pratelli:
The sharp quantitative isoperimetric inequality
Ann. of Math. (2) 2006

S. Conti, F. Maggi, S. Müller:
Rigorous derivation of Föppl's theory for clamped elastic membranes leads to relaxation
SIAM J. Math. Anal. Vol. 38, N. 2, p. 657-680, 2006

N. Fusco, F. Maggi, A. Pratelli:
The sharp quantitative Sobolev inequality for functions of bounded variation
J. Funct. Anal. 2006

F. Maggi, C. Villani:
Balls have the worst best Sobolev inequalities. Part II: Variants and extensions
Calc. Var. Partial Differential Equations (Accepted Paper) 2007

F. Maggi:
Some methods for studying stability in isoperimetric type problems
(Lecture notes (accepted in revised form on Bull. Amer. Math. Soc.)) 2007

A. Cianchi, N. Fusco, F. Maggi, A. Pratelli:
The sharp Sobolev inequality in quantitative form
Journal of the European Mathematical Society 2007

N. Fusco, F. Maggi, A. Pratelli:
Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)  2007

A. Figalli, F. Maggi, A. Pratelli:
A note on Cheeger sets
Proc. Amer. Math. Soc. 2008

A. Cianchi, N. Fusco, F. Maggi, A. Pratelli:
On the isoperimetric deficit in the Gauss space
American Journal of Mathematics (Accepted Paper) 2008

A. Figalli, F. Maggi, A. Pratelli:
A refined Brunn-Minkowski inequality for convex sets
Ann. Inst. H. Poincaré Anal. Non Linéaire 2009

A. Figalli, F. Maggi:
On the shape of liquid drops and crystals in the small mass regime
Arch. Ration. Mech. Anal. (Accepted Paper) 2010

I. Fonseca, G. Leoni, F. Maggi, M. Morini:
Exact reconstruction of damaged color images using a total variation model
Ann. Inst. H. Poincaré Anal. Non Linéaire Vol. 27, N. 5, p. 1291-1331, 2010

N. Fusco, F. Maggi, A. Pratelli:
On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density
Journal of Functional Analysis 2010

A. Figalli, F. Maggi, A. Pratelli:
A mass transportation approach to quantitative isoperimetric inequalities
Invent. Math. 2010

G. De Philippis, F. Maggi:
Sharp stability inequalities for the Plateau problem
J. Differential Geom. (Accepted Paper) 2011

F. Maggi, M. Ponsiglione, A. Pratelli:
Quantitative stability in the isodiametric inequality via the isoperimetric inequality
Trans. AMS 2011

A. Figalli, F. Maggi:
On the isoperimetric problem for radial log-convex densities
Calc. Var. Partial Differential Equations (Accepted Paper) 2012

F. Maggi:
Sets of Finite Perimeter and Geometric Variational Problems: an Introduction to Geometric Measure Theory
(Book extract) 2012

A. Figalli, F. Maggi, A. Pratelli:
A Geometric Approach to Correlation Inequalities in the Plane
Ann. Inst. Henri Poincaré Probab. Stat. 2012

A. Figalli, F. Maggi, A. Pratelli:
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation
Adv. Math. 2012

F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi:
Rigidity of equality cases in Steiner's perimeter inequality
Anal. PDE (Accepted Paper) 2013

F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi:
Essential connectedness and the rigidity problem for Gaussian
  symmetrization
J. Eur. Math. Soc. (Accepted Paper) 2013

A. Figalli, N. Fusco, F. Maggi, V. Millot, M. Morini:
Isoperimetry and stability properties of balls with respect to nonlocal energies
Comm. Math. Phys. (Accepted Paper) 2014

G. De Philippis, F. Maggi:
Dimensional estimates for singular sets in geometric variational
  problems with free boundaries
J. Reine Angew. Math. (Accepted Paper) p. 15, 2014

G. De Philippis, F. Maggi:
Regularity of free boundaries in anisotropic capillarity problems and
  the validity of Young's law
Arch. Ration. Mech. Anal. (Accepted Paper) 2014

F. Maggi, C. Mihaila:
On the shape of capillarity droplets in a container
Calc. Var. PDE (Accepted paper) p. 37, 2015

G. P. Leonardi, F. Maggi:
Improved convergence theorems for bubble clusters. II. The three-dimensional case
Indiana U Math Journal (Accepted Paper) 2015

M. Caroccia, F. Maggi:
A sharp quantitative version of Hales' isoperimetric honeycomb theorem
Journal de Mathématiques Pures et Appliquées 2015

M. Colombo, F. Maggi:
Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters
Nonlinear Analysis (Accepted Paper) 2016

G. Ciraolo, F. Maggi:
On the shape of compact hypersurfaces with almost constant mean curvature
Comm. Pure Appl. Math. (Accepted Paper) p. 33, 2016

E. Carlen, F. Maggi:
Stability for the Brunn-Minkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range non-local isoperimetry
Canadian J. Math. (Accepted Paper) 2016

F. Cavalletti, F. Maggi, A. Mondino:
Rigidity for critical points in the Levy-Gromov inequality
Math. Zeit p. 5, 2016

M. Cicalese, G. P. Leonardi, F. Maggi:
Improved convergence theorems for bubble clusters. I. The planar case
Indiana U Math Journal Vol. 65, p. 1979-2050, 2016

G. Ciraolo, A. Figalli, F. Maggi:
A quantitative analysis of metrics on $\mathbb R^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows
Int. Math. Res. Not. IMRN (Accepted Paper) p. 31, 2017

F. Maggi, E. Valdinoci:
Capillarity problems with nonlocal surface tension energies
Comm. PDE (Preprint) 2017

B. Krummel, F. Maggi:
Isoperimetry with upper mean curvature bounds and sharp stability estimates
Calc. Var. PDE (Submitted Paper) 2017

F. Cavalletti, F. Maggi, A. Mondino:
Quantitative isoperimetry à  la  Levy-Gromov
Comm. Pure and Applied Math. (Accepted Paper) 2017

S. Dipierro, F. Maggi, E. Valdinoci:
Asymptotic expansions of the contact angle in nonlocal capillarity problems
J. Nonlinear Science (Preprint) 2017

F. Maggi, R. Neumayer:
A bridge between Sobolev and Escobar inequalities and beyond
Journal of Functional Analysis (Submitted Paper) p. 26, 2017

C. De Lellis, F. Ghiraldin, F. Maggi:
A direct approach to Plateau's problem
JEMS Vol. 19, N. 8, p. 22192240, 2017

M. Delgadino, F. Maggi, C. Mihaila, R. Neumayer:
Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals
Archive for Rational Mechanics and Analysis 2017

M. Delgadino, F. Maggi:
Alexandrov's theorem revisited
Analysis & PDE 2017

M. Cicalese, G. P. Leonardi, F. Maggi:
Sharp stability inequalities for planar double bubbles
Interfaces and Free Boundaries Vol. 19, N. 3, p. 305350, 2017

A. Figalli, F. Maggi, C. Mooney:
The sharp quantitative Euclidean concentration inequality
Camb. J. Math. (Accepted Paper) 2018

G. Ciraolo, A. Figalli, F. Maggi, M. Novaga:
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
J. Reine Angew. Math. Vol. 741, p. 275-294, 2018

F. Maggi, A. Scardicchio, S. Stuvard:
Soap films with gravity and almost-minimal surfaces
Discrete Cont. Dyn. Syst. 2019

J. Bernstein, F. Maggi:
Symmetry and Rigidity of Minimal Surfaces with Plateau-like Singularities
(Preprint) 2020

F. Maggi, E. Valdinoci:
Ars Inveniendi Analytica
(Announcement) 2020

S. Dipierro, F. Maggi, E. Valdinoci:
Minimizing cones for fractional capillarity problems
(Preprint) 2020

D. King, F. Maggi, S. Stuvard:
Collapsing and the convex hull property in a soap film capillarity model
Ann. Inst. H. Poincaré Anal. Non Linéaire Vol. 38, N. 6, p. 1929-1941, 2021

D. King, F. Maggi, S. Stuvard:
Smoothness of collapsed regions in a capillarity model for soap films
Arch. Ration. Mech. Anal. Vol. 243, N. 2, p. 459-500, 2022

F. Maggi, D. Restrepo:
Uniform stability in the Euclidean isoperimetric problem for the Allen--Cahn energy
(Preprint) p. 61, 2022

D. King, F. Maggi, S. Stuvard:
Plateau's problem as a singular limit of capillarity problems
Comm. Pure Appl. Math. Vol. 75, N. 5, p. 895-969, 2022

F. Maggi, M. Novack:
Isoperimetric residues and a mesoscale flatness criterion for hypersurfaces with bounded mean curvature
(Preprint) p. 67, 2022

F. Maggi, R. Neumayer, I. Tomasetti:
Rigidity theorems for best Sobolev inequalities
(Preprint) 2022

F. Maggi, M. Santilli:
Rigidity and compactness with constant mean curvature in warped product  manifolds
(preprint) 2023

N. Fusco, F. Maggi, M. Morini, M. Novack:
Rigidity and large volume residues in exterior isoperimetry for convex sets
(Preprint) 2023

F. Maggi, M. Novack, D. Restrepo:
Plateau borders in soap films and Gauss' capillarity theory
(Preprint) 2023

F. Maggi, M. Novack, D. Restrepo:
A hierarchy of Plateau problems and the approximation of Plateau's laws via the Allen--Cahn equation
(Preprint) p. 59, 2023

F. Maggi:
Optimal Mass Transport on Euclidean Spaces
(Book extract) 2023