A. Figalli:
Il problema di Bernstein e una congettura di De Giorgi
(Degree Thesis (3rd year)) p. 69, 2004
A. Figalli:
Existence, uniqueness and regularity of optimal transport maps
SIAM Journal on Mathematical Analysis (Accepted Paper) 2006
A. Figalli:
Trasporto ottimale su varietà non compatte
(Degree Thesis (5th year)) p. 99, 2006
A. Abbondandolo, A. Figalli:
High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
J. Differential Equations (Accepted Paper) 2006
A. Figalli:
The Monge problem on non-compact manifolds
Rend. Sem. Mat. Univ. Padova (Accepted Paper) 2006
A. Figalli:
Optimal transportation and action-minimizing measures
(Ph.D. Thesis) p. 251, 2007
A. Fathi, A. Figalli:
Optimal transportation on non-compact manifolds
Israel J. Math. (Accepted Paper) 2007
A. Figalli, C. Villani:
Strong displacement convexity on Riemannian manifolds
Mathematische Zeitschrift (Accepted Paper) 2007
A. Figalli:
A simple proof of the Morse-Sard Theorem in Sobolev Spaces
Proc. Amer. Math. Soc. (Accepted Paper) 2007
L. Ambrosio, A. Figalli:
On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations
Calc. Var. Partial Differential Equations (Accepted Paper) 2007
A. Figalli:
Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
J. Funct. Anal. (Accepted Paper) 2007
M. Bernot, A. Figalli:
Synchronized traffic plans and stability of optima
ESAIM: COCV (Accepted Paper) 2007
L. Ambrosio, A. Figalli:
Geodesics in the space of measure-preserving maps and plans
Arch. Rat. Mech. Anal. (Accepted Paper) 2007
A. Figalli, F. Maggi, A. Pratelli:
A note on Cheeger sets
Proc. Amer. Math. Soc. 2008
A. Figalli:
A geometric lower bound on Grad's number
ESAIM Control Optim. Calc. Var. (Accepted Paper) 2008
A. Figalli, N. Juillet:
Absolute continuity of Wasserstein geodesics in the Heisenberg group
J. Funct. Anal. (Accepted Paper) 2008
A. Fathi, A. Figalli, L. Rifford:
On the Hausdorff Dimension of the Mather Quotient
Comm. Pure Appl. Math. (Accepted Paper) 2008
A. Figalli, C. Villani:
Optimal Transport and Curvature
(Lecture Notes) 2008
A. Figalli, C. Villani:
An approximation lemma about the cut locus, with applications in optimal transport theory
Methods Appl. Anal. (Accepted Paper) 2008
A. Abbondandolo, A. Figalli:
Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index
Journal of Fixed Point Theory and Applications (Accepted Paper) 2008
M. Bernot, A. Figalli, F. Santambrogio:
Generalized solutions for the Euler equations in one and two dimensions
J. Math. Pures Appl. (Accepted Paper) 2008
A. Figalli, R. Philipowski:
Convergence to the viscous porous medium equation and propagation of chaos
ALEA Lat. Am. J. Probab. Math. Stat. (Accepted Paper) 2008
L. Ambrosio, A. Figalli:
On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions
J. Funct. Anal. (Accepted Paper) 2008
A. Figalli:
The optimal partial transport problem
Arch. Ration. Mech. Anal. (Accepted Paper) 2008
A. Figalli, G. Loeper:
$C^1$ regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two
Calc. Var. Partial Differential Equations (Accepted Paper) 2008
L. Ambrosio, G. Crippa, A. Figalli, L. V. Spinolo:
Some new well-posedness results for continuity and transport equations, and applications to the chromatography system
SIAM J. Math. Anal. Vol. 41, N. 5, p. 1890-1920, 2009
A. Figalli, N. Gigli:
Local semiconvexity of Kantorovich potentials on non-compact manifolds
ESAIM Control Optim. Calc. Var. (Accepted Paper) 2009
A. Figalli:
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions
() 2009
L. Ambrosio, A. Figalli:
Lecture notes on variational models for incompressible Euler equations
(Lecture notes) 2009
A. Figalli, L. Rifford:
Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S^2
Comm. Pure Appl. Math. (Accepted Paper) 2009
A. Figalli, L. Rifford:
Mass Transportation on Sub-Riemannian Manifolds
Geom. Funct. Anal. (Accepted Paper) 2009
A. Figalli:
A note on the regularity of the free boundaries in the optimal partial transport problem
Rend. Circ. Mat. Palermo (Accepted Paper) 2009
A. Figalli:
Regularity properties of optimal maps between nonconvex domains in the plane
Comm. Partial Differential Equations (Accepted Paper) 2009
A. Figalli, N. Gigli:
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions
J. Math. Pures Appl. (Accepted Paper) 2009
A. Figalli:
Regularity of optimal transport maps (after Ma-Trudinger-Wang and Loeper)
(S\'eminaire Bourbaki) 2009
A. Figalli:
Optimal transport, Euler equations, Mather and DiPerna-Lions theories
(Mémoire HDR) p. 53, 2009
A. Figalli:
Optimal transport. Old and new. [book review]
Bull. Amer. Math. Soc. (Accepted Paper) 2009
L. Desvillettes, A. Figalli:
Cédric Villani reçoit un prix de la Société Mathématique Européenne
Gazette SMF 2009
A. Figalli:
On flows of $H^{3/2}$-vector fields on the circle
Math. Ann. (Accepted Paper) 2009
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
L. Ambrosio, G. Crippa, A. Figalli, L. V. Spinolo:
Existence and uniqueness results for the continuity equation and applications to the chromatography system
IMA Vol. Math. Appl., Springer (Proceedings) 2010
A. Figalli, Y. H. Kim, R. J. McCann:
When is multidimensional screening a convex program?
J. Econom. Theory (Accepted Paper) 2010
L. Ambrosio, A. Figalli:
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Ann. Fac. Sci. Toulouse Math. (Accepted Paper) 2010
J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepev:
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
Duke Math. J. (Accepted Paper) 2010
L. Ambrosio, A. Figalli:
Almost everywhere well-posedness of continuity equations with measure initial data
C. R. Math. Acad. Sci. Paris (Accepted Paper) 2010
A. Figalli, Y. H. Kim:
Partial regularity of Brenier solutions of the Monge-Ampère equation
Discrete Contin. Dyn. Syst. Series A (Accepted Paper) 2010
A. Figalli, W. Gangbo, T. Yolcu:
A variational method for a class of parabolic PDEs
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (Accepted Paper) 2010
A. Figalli, L. Rifford, C. Villani:
On the Ma-Trudinger-Wang curvature on surfaces
Calc. Var. Partial Differential Equations (Accepted Paper) 2010
A. Figalli:
Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals
Contemp. Math. (Proceedings) 2010
A. Figalli, F. Maggi, A. Pratelli:
A mass transportation approach to quantitative isoperimetric inequalities
Invent. Math. 2010
C. Bjorland, L. Caffarelli, A. Figalli:
Non-Local Tug-of-War and the Infinity Fractional Laplacian
Comm. Pure Appl. Math. (Accepted Paper) 2011
J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepev:
Confinement in nonlocal interaction equations
Nonlinear Anal. (Accepted Paper) 2011
L. Ambrosio, A. Figalli, G. Friesecke, J. Giannoulis, T. Paul:
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Comm. Pure Appl. Math. (Accepted Paper) 2011
A. Figalli, L. Rifford, C. Villani:
Nearly round spheres look convex
Amer. J. Math. (Accepted Paper) 2011
A. Figalli, L. Rifford, C. Villani:
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds
Tohoku Math. J. (Accepted Paper) 2011
A. Figalli, Y. H. Kim, R. J. McCann:
Regularity of optimal transport maps on multiple products of spheres
J. Eur. Math. Soc. (JEMS) (Accepted Paper) 2011
A. Figalli, L. Rifford, C. Villani:
Tangent cut loci on surfaces
Differential Geom. Appl. (Accepted Paper) 2011
A. Figalli, M. Ligabò, T. Paul:
Semiclassical limit for mixed states with singular and rough potentials
Indiana Univ. Math. J. (Accepted Paper) 2011
A. Figalli, Y. Ge:
Isoperimetric-type inequalities on constant curvature manifolds
Adv. Calc. Var. (Accepted Paper) 2011
L. Caffarelli, A. Figalli:
Regularity of solutions to the parabolic fractional obstacle problem
J. Reine Angew. Math. 2011
A. Figalli, E. Indrei:
A sharp stability result for the relative isoperimetric inequality inside convex cones
J. Geom. Anal. (Accepted Paper) 2011
A. Figalli, V. Mandorino:
Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials
Discrete Contin. Dyn. Syst. Series A (Accepted Paper) 2011
S. Daneri, A. Figalli:
Variational models for the incompressible Euler equations
(Lecture Notes) 2011
M. Bonforte, A. Figalli:
Total Variation Flow and Sign Fast Diffusion in one dimension
J. Differential Equations (Accepted Paper) 2012
A. Figalli, F. Maggi:
On the isoperimetric problem for radial log-convex densities
Calc. Var. Partial Differential Equations (Accepted Paper) 2012
C. Bjorland, L. Caffarelli, A. Figalli:
Non-Local Gradient Dependent Operators
Adv. Math. (Accepted Paper) 2012
A. Figalli:
Stability in geometric and functional inequalities
(Proceedings of the 6ECM) 2012
E. Carlen, A. Figalli:
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
Duke Math. J. (Accepted Paper) 2012
B. Barrios, A. Figalli, E. Valdinoci:
Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (Accepted Paper) 2012
A. Figalli:
Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations
(Proceedings) 2012
L. Ambrosio, A. Figalli, E. Runa:
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. (Accepted Paper) 2012
A. Figalli, L. Rifford:
Aubry sets, Hamilton-Jacobi equations, and the Mañé Conjecture
Contemp. Math. (Proceedings ) 2012
M. Colombo, A. Figalli:
Regularity results for very degenerate elliptic equations
J. Math. Pures Appl. (Accepted Paper) 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
G. De Philippis, A. Figalli:
Sobolev regularity for Monge-Ampère type equations
SIAM J. Math. Anal. (Accepted Paper) 2012
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
A global existence result for the semigeostrophic equations in three
dimensional convex domains
Discrete Contin. Dyn. Syst. (Accepted Paper) 2012
G. De Philippis, A. Figalli, O. Savin:
A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere
equation
Math. Ann. (Accepted Paper) 2012
G. De Philippis, A. Figalli:
Second order stability for the Monge-Ampere equation and strong Sobolev
convergence of optimal transport maps
Anal. PDE (Accepted Paper) 2012
G. De Philippis, A. Figalli:
$W^{2,1}$ regularity for solutions of the Monge-Ampère equation
Invent. Math. (Accepted Paper) 2012
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
Existence of Eulerian solutions to the semigeostrophic equations in
physical space: the 2-dimensional periodic case
Comm. Partial Differential Equations (Accepted Paper) 2012
A. Figalli, C. Klein, P. Markovich, C. Sparber:
WKB analysis of Bohmian dynamics
Comm. Pure Appl. Math. (Accepted Paper) 2013
S. Dipierro, A. Figalli, G. Palatucci, E. Valdinoci:
Asymptotics of the $s$-perimeter as $s \searrow 0$
Discrete Contin. Dyn. Syst. Vol. 33, N. 7, p. 2777-2790, 2013
A. Figalli, Y. H. Kim, R. J. McCann:
Hölder continuity and injectivity of optimal maps
Arch. Ration. Mech. Anal. (Accepted Paper) 2013
A. Figalli, D. Jerison:
How to recognize convexity of a set from its marginals
J. Funct. Anal. (Accepted Paper) 2013
A. Figalli, Y. H. Kim, R. J. McCann:
On supporting hyperplanes to convex bodies
Methods Appl. Anal. (Accepted Paper) 2013
A. Figalli, L. Rifford:
Closing Aubry sets I
Comm. Pure Appl. Math. (Accepted Paper) 2013
A. Figalli, L. Rifford:
Closing Aubry sets II
Comm. Pure Appl. Math. (Accepted Paper) 2013
G. De Philippis, A. Figalli:
Optimal regularity of the convex envelope
Trans. Amer. Math. Soc. (Accepted Paper) 2013
M. Colombo, A. Figalli:
An excess-decay result for a class of degenerate elliptic equations
Discrete Contin. Dyn. Syst. (Accepted Paper) 2013
G. De Philippis, A. Figalli:
Higher integrability for minimizers of the Mumford-Shah functional
Arch. Ration. Mech. Anal. (Accepted Paper) 2013
A. Figalli, H. Shahgholian:
A general class of free boundary problems for fully nonlinear elliptic equations
Arch. Ration. Mech. Anal. (Accepted Paper) 2014
A. Figalli, H. Shahgholian:
A general class of free boundary problems for fully nonlinear parabolic equations
Ann. Mat. Pura Appl. (Accepted Paper) 2014
A. Figalli:
Quantitative stability results for the Brunn-Minkowski inequality
(Proceedings ICM 2014) 2014
S. Dipierro, A. Figalli, E. Valdinoci:
Strongly nonlocal dislocation dynamics in crystals
Comm. Partial Differential Equations (Accepted Paper) 2014
A. Figalli, D. Jerison:
Quantitative stability for sumsets in $R^n$
J. Eur. Math. Soc. (JEMS) (Accepted Paper) 2014
G. Contreras, A. Figalli, L. Rifford:
Generic hyperbolicity of Aubry sets on surfaces
Invent. Math. (Accepted Paper) 2014
A. Figalli:
Stability results for the Brunn-Minkowski inequality
Colloquium De Giorgi 2013-2014 (Accepted Paper) 2014
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
A. Figalli, T. Gallouët, L. Rifford:
On the convexity of injectivity domains on nonfocal manifolds
SIAM J. Math. Anal. (Accepted Paper) 2014
G. De Philippis, A. Figalli:
Partial regularity results in optimal transportation
(Springer INdAM series) 2014
S. Chen, A. Figalli:
Boundary $\varepsilon$-regularity in optimal transportation
Adv. Math. (Accepted Paper) 2014
A. Figalli, E. Valdinoci:
Regularity and Bernstein-type results for nonlocal minimal surfaces
J. Reine Angew. Math. (Accepted Paper) 2014
G. De Philippis, A. Figalli:
A note on the dimension of the singular set in free interface problems
Differential Integral Equations (Accepted Paper) 2014
G. De Philippis, A. Figalli:
The Monge-Ampère equation and its link to optimal transportation
Bull. Amer. Math. Soc. (Accepted Paper) 2014
G. De Philippis, A. Figalli:
Partial Regularity for optimal transport maps
Publ. Math. Inst. Hautes Études Sci. (Accepted Paper) 2014
A. Figalli, H. Shahgholian:
An overview of unconstrained free boundary problems
Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (Accepted Paper) 2015
L. Ambrosio, J. Bourgain, H. Brezis, A. Figalli:
$BMO$-type norms related to the perimeter of sets
Comm. Pure Appl. Math. (Accepted Paper) 2015
A. Figalli:
Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère
CIME Lecture Notes (Lecture notes) 2015
F. Bekermam, A. Figalli, A. Guionnet:
Transport maps for $\beta$-matrix models and Universality
Comm. Math. Phys. (Accepted Paper) 2015
L. Ambrosio, M. Colombo, A. Figalli:
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Arch. Ration. Mech. Anal. (Accepted Paper) 2015
A. Figalli, A. Pelayo:
On the density function on moduli spaces of toric 4-manifolds
Adv. Geom. (Accepted Paper) 2015
A. Figalli, Y. Jhaveri, C. Mooney:
Nonlinear bounds in Hölder spaces for the Monge-Ampère equation
J. Funct. Anal. (Accepted Paper) 2015
S. Chen, A. Figalli:
Stability results on the smoothness of optimal transport maps with general costs
J. Math. Pures Appl. (Accepted Paper) 2016
M. Bonforte, A. Figalli, X. Ros-Oton:
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains
Comm. Pure Appl. Math. (Accepted Paper) 2016
A. Figalli:
Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand
J. Diff. Geom. (Accepted Paper) 2016
E. Baer, A. Figalli:
Characterization of isoperimetric sets inside almost-convex cones
Discrete Contin. Dyn. Syst. (Accepted Paper) 2016
A. Figalli, D. Gomes, D. Marcon:
Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations
Calc. Var. Partial Differential Equations (Accepted Paper) 2016
A. Figalli:
A transportation approach to universality in random matrix theory
Boll. Unione Mat. Ital. (Lecture Notes) 2016
A. Figalli, D. Jerison:
Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume
Chin. Ann. Math. (Accepted Paper) 2016
A. Figalli, A. Guionnet:
Universality in several-matrix models via approximate transport maps
Acta Math. (Accepted Paper) 2016
A. Figalli, R. Neumayer:
Gradient stability for the Sobolev inequality: the case $p\geq 2$
J. Eur. Math. Soc. (JEMS) (Accepted Paper) 2016
A. Figalli, J. Palmer, A. Pelayo:
Symplectic G-capacities and integrable systems
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (Accepted Paper) 2016
J. A. Carrillo, A. Figalli, F. S. Patacchini:
Geometry of minimizers for the interaction energy with mildly repulsive potentials
Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) 2016
M. Cozzi, A. Figalli:
Regularity theory for local and nonlocal minimal surfaces: an overview
CIME Lecture Notes (Lecture Notes) 2016
G. De Philippis, A. Figalli:
Rigidity and stability of Caffarelli's log-concave perturbation theorem
Nonlinear Anal. (Accepted Paper) 2016
S. Chen, A. Figalli:
Partial $W^{2,p}$ regularity for optimal transport maps
J. Funct. Anal. (Accepted Paper) 2017
A. Figalli, B. Krummel, X. Ros-Oton:
On the regularity of the free boundary in the p-Laplacian obstacle problem
J. Differential Equations (Accepted Paper) 2017
M. Colombo, A. Figalli, Y. Jhaveri:
Lipschitz changes of variables between perturbations of log-concave measures
Ann. Sc. Norm. Super. Pisa Cl. Sci. (Accepted Paper) 2017
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
A. Figalli, D. Jerison:
Quantitative stability for the Brunn-Minkowski inequality
Adv. Math. (Accepted Paper) 2017
B. Barrios, A. Figalli, X. Ros-Oton:
Global regularity for the free boundary in the obstacle problem for the fractional Laplacian
Amer. J. Math. (Accepted Paper) 2017
L. Ambrosio, M. Colombo, A. Figalli:
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Duke Math. J. (Accepted Paper) 2017
B. Barrios, A. Figalli, X. Ros-Oton:
Free boundary regularity in the parabolic fractional obstacle problem
Comm. Pure Appl. Math. (Accepted Paper) 2017
A. Figalli, M. J. Kang, J. Morales:
Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow
Arch. Ration. Mech. Anal. (Accepted Paper) 2017
A. Figalli, C. Mooney:
An obstacle problem for conical deformations of thin elastic sheets
Arch. Ration. Mech. Anal. (Accepted Paper) 2017
M. Bonforte, A. Figalli, J. L. Vazquez:
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains
Anal. PDE (Accepted Paper) 2017
L. Caffarelli, F. Cagnetti, A. Figalli:
Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive zone models
(Submitted Paper) 2017
M. Bonforte, A. Figalli, J. L. Vazquez:
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations
Calc. Var. Partial Differential Equations (Accepted Paper) 2018
A. Figalli, F. Maggi, C. Mooney:
The sharp quantitative Euclidean concentration inequality
Camb. J. Math. (Accepted Paper) 2018
A. Figalli:
On the Continuity of Center-Outward Distribution and Quantile Functions
Nonlinear Anal. (Accepted Paper) 2018
A. Figalli:
Free boundary regularity in obstacle problems
(Lecture Notes) 2018
A. Figalli:
On the Monge-Ampère equation
(Lecture Notes) 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
A. Figalli:
Regularity of interfaces in phase transitions via obstacle problems
Proceedings ICM 2018 (Proceedings) 2018
A. Figalli, J. Serra:
On the fine structure of the free boundary for the classical obstacle problem
Invent. Math. (Accepted Paper) 2018