# Published/accepted papers

- Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)

*Duke Math. J.*, to appear. - Strong stability for the Wulff inequality with a crystalline norm (with Y. Ru-Ya Zhang)
*Comm. Pure Appl. Math.*, to appear - A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces (with D. Jerison)
*Ann. Sci. Éc. Norm. Supér.**(4)*54 (2021), no. 1, 235–257. - Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (with M. Bonforte)
*Comm. Pure Appl. Math.*74 (2021), no. 4, 744–789. - Generic regularity of free boundaries for the obstacle problem (with X. Ros-Oton and J. Serra)
*Publ. Math. Inst. Hautes Études Sci.*132 (2020), 181–292. - Stable solutions to semilinear elliptic equations are smooth up to dimension 9 (with X. Cabré, X. Ros-Oton and J. Serra)
*Acta Math.*224 (2020), no. 2, 187–252. - Symmetry results for critical anisotropic
*p*-Laplacian equations in convex cones (with G. Ciraolo and A. Roncoroni)*Geom. Funct. Anal.*30 (2020), no. 3, 770-803. - On the obstacle problem for the 1D wave equation (with X. Fernández-Real)
*Math. Eng.*2 (2020), no. 4, 584-597. - Optimal regularity and structure of the free boundary for minimizers in cohesive zone models (with L. Caffarelli and F. Cagnetti)
*Arch. Ration. Mech. Anal.*237 (2020), no. 1, 299–345. - On the sharp stability of critical points of the Sobolev inequality (with F. Glaudo)
*Arch. Ration. Mech. Anal.*237 (2020), no. 1, 201–258. - On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1
(with J. Serra)
*Invent. Math.*219 (2020), no. 1, 153-177. - Regularity of monotone transport maps between unbounded domains (with D. Cordero-Erausquin)
*Discrete Contin. Dyn. Syst.*39 (2019), no. 12, 7101-7112. - Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations (with J. E. M. Braga and D. Moreira)
*Comm. Math. Phys.*367 (2019), no. 1, 1-32. - On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)
*Invent. Math.*215 (2019), no. 1, 311-366. - A rigorous derivation from the kinetic cucker-smale model to the pressureless euler system with nonlocal alignment (with M.-J. Kang)
*Anal. PDE*12 (2019), no. 3, 843-866. - Gradient stability for the Sobolev inequality: the case p≥2 (with R. Neumayer)
*J. Eur. Math. Soc. (JEMS)*21 (2019), no. 2, 319-354. - On the Continuity of Center-Outward Distribution and Quantile Functions
*Nonlinear Anal.*177 (2018), part B, 413-421. - Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (with M. Bonforte and J. L. Vázquez)
*Calc. Var. Partial Differential Equations*57 (2018), no. 2, Art. 57, 34 pp. - The sharp quantitative Euclidean concentration inequality (with F. Maggi and C. Mooney)
*Camb. J. Math.*6 (2018), no. 1, 59-87. - Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (with M. Bonforte and J. L. Vázquez)
*Anal. PDE*11 (2018), no. 4, 945-982. - An obstacle problem for conical deformations of thin elastic sheets (with C. Mooney)
*Arch. Ration. Mech. Anal.*228 (2018), no. 2, 401-429. - Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow (with M.-J. Kang and J. Morales)
*Arch. Ration. Mech. Anal.*227 (2018), no. 3, 869-896. - Free boundary regularity in the parabolic fractional obstacle problem (with B. Barrios and X. Ros-Oton)
*Comm. Pure Appl. Math.*71 (2018), no. 10, 2129-2159. - Global regularity for the free boundary in the obstacle problem for the fractional Laplacian (with B. Barrios and X. Ros-Oton)
*Amer. J. Math.*140 (2018), no. 2, 415-447. - A quantitative analysis of metrics on R^n with almost constant positive scalar curvature, with applications to fast diffusion flows (with G. Ciraolo and F. Maggi)

*Int. Math. Res. Not. IMRN*(2018), no. 21, 6780-6797. - Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature (with G. Ciraolo, F. Maggi, and M. Novaga)
*J. Reine Angew. Math.*741 (2018), 275-294. - Symplectic G-capacities and integrable systems (with J. Palmer and Á. Pelayo)
*Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)*18 (2018), no. 1, 65-103. - On the Lagrangian structure of transport equations: the Vlasov-Poisson system (with L. Ambrosio and M. Colombo)
*Duke Math. J.*166 (2017), no. 18, 3505-3568. - Geometry of minimizers for the interaction energy with mildly repulsive potentials (with J. A. Carrillo and F. S. Patacchini)
*Ann. Inst. H.**Poincaré**Anal. Non Linéaire*34 (2017), no. 5, 1299-1308. - Lipschitz changes of variables between perturbations of log-concave measures (with M. Colombo and Y. Jhaveri)
*Ann. Sc. Norm. Super. Pisa Cl. Sci.*,*(5)*17 (2017), no. 4, 1491-1519. - Regularity and Bernstein-type results for nonlocal minimal surfaces (with E. Valdinoci)
*J. Reine Angew. Math.*729 (2017), 263-273. - Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains (with M. Bonforte and X. Ros-Oton)

*Comm. Pure Appl. Math.*70 (2017), no. 8, 1472-1508. - Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand

*J. Diff. Geom.*106 (2017), no. 3, 371-391. - Quantitative stability for the Brunn-Minkowski inequality (with D. Jerison)
*Adv. Math.*314 (2017), 1-47. - On the regularity of the free boundary in the p-Laplacian obstacle problem (with B. Krummel and X. Ros-Oton)
*J. Differential Equations*263 (2017), no. 3, 1931-1945. - Partial W^{2,p} regularity for optimal transport maps (with S. Chen)

*J. Funct. Anal.*272 (2017), no. 11, 4588-4605. - Rigidity and stability of Caffarelli's log-concave perturbation theorem (with G. De Philippis)

*Nonlinear Anal.*154 (2017), 59-70. - Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume (with D. Jerison)
*Chin. Ann. Math. Ser. B*38 (2017), no. 2, 393-412. - Characterization of isoperimetric sets inside almost-convex cones (with E. Baer)
*Discrete Contin. Dyn. Syst.*37 (2017), no. 1, 1-14. - Universality in several-matrix models via approximate transport maps (with A. Guionnet)
*Acta Math.*217 (2016), no. 1, 81-176. - Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations (with D. Gomes and D. Marcon)

*Calc. Var. Partial Differential Equations*55 (2016), no. 4, 55-79. - Stability results on the smoothness of optimal transport maps with general costs (with S. Chen)

*J. Math. Pures Appl.**(9)*106 (2016), no. 2, 280-295. - Nonlinear bounds in Hölder spaces for the Monge-Ampère equation (with Y. Jhaveri and C. Mooney)

*J. Funct. Anal.*270 (2016), no. 10, 3808-3827. - On the density function on moduli spaces of toric 4-manifolds (with Á. Pelayo)

*Adv. Geom.*16 (2016), no. 3, 291-300. - BMO-type norms related to the perimeter of sets (with L. Ambrosio, J. Bourgain, and H. Brezis)

*Comm. Pure Appl. Math.*69 (2016), no. 6, 1062-1086. - Existence and uniqueness of maximal regular flows for non-smooth vector fields (with L. Ambrosio and M. Colombo)

*Arch. Ration. Mech. Anal.*218 (2015), no. 2, 1043-1081. - Transport maps for β-matrix models and universality (with F. Bekerman and A. Guionnet)

*Comm. Math. Phys.*338 (2015), no. 2, 589-619. - A note on the dimension of the singular set in free interface problems (with G. De Philippis)

*Differential Integral Equations*28 (2015), 523-536. - Boundary ε-regularity in optimal transportation (with S. Chen)

*Adv. Math.*273 (2015), 540-567. - On the convexity of injectivity domains on nonfocal manifolds (with T. Gallouët and L. Rifford)

*SIAM J. Math. Anal.*47 (2015), no. 2, 969-1000. - Partial regularity for optimal transport maps (with G. De Philippis)

*Publ. Math. Inst. Hautes Études Sci.*121 (2015), 81-112. - Isoperimetry and stability properties of balls with respect to nonlocal energies (with N. Fusco, F. Maggi, V. Millot, and M. Morini)

*Comm. Math. Phys.*336 (2015), no. 1, 441-507. - Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)

*Invent. Math.*200 (2015), no. 1, 201-261. - Quantitative stability for sumsets in R
^{n}(with D. Jerison)

*J. Eur. Math. Soc. (JEMS)*17 (2015), no. 5, 1079-1106. - A general class of free boundary problems for fully nonlinear parabolic equations (with H. Shahgholian)

*Ann. Mat. Pura Appl. (4)*194 (2015), no. 4, 1123-1134. - Optimal regularity of the convex envelope (with G. De Philippis)

*Trans. Amer. Math. Soc.*367 (2015), no. 6, 4407-4422. - Closing Aubry sets II (with L. Rifford)

*Comm. Pure Appl. Math.*68 (2015), no. 3, 345-412. - Closing Aubry sets I (with L. Rifford)

*Comm. Pure Appl. Math.*68 (2015), no. 2, 210-285. - Strongly nonlocal dislocation dynamics in crystals (with S. Dipierro and E. Valdinoci)

*Comm. Partial Differential Equations*39 (2014), no. 12, 2351-2387. - A general class of free boundary problems for fully nonlinear elliptic equations (with H. Shahgholian)

*Arch. Ration. Mech. Anal.*213 (2014), no. 1, 269-286. - Higher integrability for minimizers of the Mumford-Shah functional (with G. De Philippis)

*Arch. Ration. Mech. Anal.*213 (2014), no. 2, 491-502. - An excess-decay result for a class of degenerate elliptic equations (with M. Colombo)

*Discrete Contin. Dyn. Syst. Ser. S*7 (2014), no. 4, 631-652. - How to recognize convexity of a set from its marginals (with D. Jerison)

*J. Funct. Anal.*266 (2014), no. 3, 1685-1701. - Regularity results for very degenerate elliptic equations (with M. Colombo)

*J. Math. Pures Appl. (9)*101 (2014), no. 1, 94-117. - WKB analysis of Bohmian dynamics (with C. Klein, P. Markowich, and C. Sparber)

*Comm. Pure Appl. Math.*67 (2014), no. 4, 581-620. - A global existence result for the semigeostrophic equations in three dimensional convex domains (with L. Ambrosio, M. Colombo, and G. De Philippis)

*Discrete Contin. Dyn. Syst.*34 (2014), no. 4, 1251-1268. - Bootstrap regularity for integro-differential operators, and its application to nonlocal minimal surfaces (with B. Barrios Barrera and E. Valdinoci)

*Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)*13 (2014), no. 3, 609-639. - A geometric approach to correlation inequalities in the plane (with F. Maggi and A. Pratelli)

*Ann. Inst. H. Poincaré Probab. Stat.*50 (2014), no. 1, 1-14. - On supporting hyperplanes to convex bodies (with Y.-H. Kim and R. J. McCann)

*Methods Appl. Anal.*20 (2013), no. 3, 261-271. - Sobolev regularity for Monge-Ampère type equations (with G. De Philippis)

*SIAM J. Math. Anal.*45 (2013), no. 3, 1812-1824. - Hölder continuity and injectivity of optimal maps (with Y.-H. Kim and R. J. McCann)

*Arch. Ration. Mech. Anal.*209 (2013), no. 3, 747-795. - On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to half-spaces (with L. Ambrosio and E. Runa)

*Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.*24 (2013), no. 1, 111-122. - Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps (with G. De Philippis)

*Anal. PDE*6 (2013), no. 4, 993-1000. - A note on interior W
^{2,1+epsilon}estimates for the Monge-Ampère equation (with G. De Philippis and O. Savin)

*Math. Ann.*357 (2013), no. 1, 11-22. - Asymptotics of the s-perimeter as s --> 0 (with S. Dipierro, G. Palatucci, and E. Valdinoci)

*Discrete Contin. Dyn. Syst.*33 (2013), no. 7, 2777-2790. - On the isoperimetric problem for radial log-convex densities (with F. Maggi)

*Calc. Var. Partial Differential Equations*48 (2013), no. 3-4, 447-489. - Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation (with E. Carlen)

*Duke Math. J.*162 (2013), no. 3, 579-625. - Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (with F. Maggi and A. Pratelli)

*Adv. Math.*242 (2013), 80-101. - W
^{2,1}regularity for solutions of the Monge-Ampère equation (with G. De Philippis)

*Invent. Math.*192 (2013), no. 1, 55-69. - Regularity of solutions to the parabolic fractional obstacle problem (with L. Caffarelli)

*J. Reine Angew. Math.*680 (2013), 191-233. - A sharp stability result for the relative isoperimetric inequality inside convex cones (with E. Indrei)

*J. Geom. Anal.*23 (2013), no. 2, 938-969. - Regularity of optimal transport maps on multiple products of spheres (with Y.-H. Kim and R. J. McCann)

*J. Eur. Math. Soc. (JEMS)*15 (2013), no. 4, 1131-1166. - Non-Local Gradient Dependent Operators (with C. Bjorland and L. Caffarelli)

*Adv. Math.*230 (2012), no. 4-6, 1859-1894. - Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (with L. Ambrosio, M. Colombo, and G. De Philippis)

*Comm. Partial Differential Equations*37 (2012), no. 12, 2209-2227. - Total Variation Flow and Signed Fast Diffusion in one dimension (with M. Bonforte)

*J. Differential Equations*252 (2012), no. 8, 4455-4480. - Semiclassical limit for mixed states with singular and rough potentials (with M. Ligabò and T. Paul)

*Indiana Univ. Math. J.*61 (2012), no. 1, 193-222. - Confinement in nonlocal interaction equations (with J. A. Carrillo, M. Di Francesco, T. Laurent, and D. Slepcev)

*Nonlinear Anal.*75 (2012), no. 2, 550-558. - Isoperimetric-type inequalities on constant curvature manifolds (with Y. Ge)

*Adv. Calc. Var.*5 (2012), no. 3, 251-284. - Non-Local Tug-of-War and the Infinity Fractional Laplacian (with C. Bjorland and L. Caffarelli)

*Comm. Pure Appl. Math.*65 (2012), no. 3, 337-380. - Nearly round spheres look convex (with L. Rifford and C. Villani)

*Amer. J. Math.*134 (2012), no. 1, 109-139. - Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds (with L. Rifford and C. Villani)

*Tohoku Math. J. (2)*63 (2011), no. 4, 855-876. Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (with L. Ambrosio, G. Friesecke, J. Giannoulis, and T. Paul)

*Comm. Pure Appl. Math.*64 (2011), no. 9, 1199-1242.- Tangent cut loci on surfaces (with L. Rifford and C. Villani)

*Differential Geom. Appl.*29 (2011), no. 2, 154-159. - When is multidimensional screening a convex program? (with Y.-H. Kim and R. J. McCann)

*J. Econom. Theory*146 (2011), no. 2, 454-478. - Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (with L. Ambrosio)

*Ann. Fac. Sci. Toulouse Math. (6)*20 (2011), no. 2, 407-438. - On the shape of liquid drops and crystals in the small mass regime (with F. Maggi)

*Arch. Ration. Mech. Anal.*201 (2011), no. 1, 143-207. - Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials (with V. Mandorino)

*Discrete Contin. Dyn. Syst.*31 (2011), no. 4, 1325-1346. - Global in time measure-valued solutions and finite-time aggregation for nonlocal interaction equations (with J. A. Carrillo, M. Di Francesco, T. Laurent, and D. Slepcev)

*Duke Math. J.*156 (2011), no. 2, 229-271. - A variational method for a class of parabolic PDEs (with W. Gangbo and T. Yolcu)

*Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)*10 (2011), no. 1, 207-252. - Local semiconvexity of Kantorovich potentials on non-compact manifolds (with N. Gigli)
*ESAIM Control Optim. Calc. Var.*17 (2011), no. 3, 648-653. - A mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
*Invent. Math.*182 (2010), no. 1, 167-211. - Partial regularity of Brenier solutions of the Monge-Ampère equation (with Y.-H. Kim)

*Discrete Contin. Dyn. Syst.*28 (2010), no. 2, 559-565. - Almost everywhere well-posedness of continuity equations with measure initial data (with L. Ambrosio)

*C. R. Math. Acad. Sci. Paris*348 (2010), no. 5-6, 249-252. - On the Ma-Trudinger-Wang curvature on surfaces (with L. Rifford and C. Villani)

*Calc. Var. Partial Differential Equations*39 (2010), no. 3, 307-332. - A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (with N. Gigli)

*J. Math. Pures Appl.*94 (2010), no. 2, 107-130. - Regularity properties of optimal maps between nonconvex domains in the plane

*Comm. Partial Differential Equations*35 (2010), no. 3, 465-479. - On flows of H
^{3/2}-vector fields on the circle

*Math. Ann.*347 (2010), no. 1, 43-57. - Mass Transportation on Sub-Riemannian Manifolds (with L. Rifford)

*Geom. Funct. Anal.*20 (2010), no. 1, 124-159. - The optimal partial transport problem

*Arch. Ration. Mech. Anal.*195 (2010), no. 2, 533-560. - Optimal transportation on non-compact manifolds (with A. Fathi)

*Israel J. Math.*175 (2010), no. 1, 1-59. - Some new well-posedness results for continuity and transport equations, and applications to the chromatography system (with L. Ambrosio, G. Crippa, and L. V. Spinolo)

*SIAM J. Math. Anal.*41 (2009), no. 5, 1890-1920. - A refined Brunn-Minkowski inequality for convex sets (with F. Maggi and A. Pratelli)

*Ann. Inst. H. Poincaré Anal. Non Linéaire*26 (2009), no. 6, 2511-2519. - Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S
^{2}(with L. Rifford)

*Comm. Pure Appl. Math.*62 (2009), no. 12, 1670-1706. - A note on the regularity of the free boundaries in the optimal partial transport problem

*Rend. Circ. Mat. Palermo*58 (2009), no. 2, 283-286. - C
^{1}regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two (with G. Loeper)

*Calc. Var. Partial Differential Equations*35 (2009), no. 4, 537-550. - A note on Cheeger sets (with F. Maggi and A. Pratelli)

*Proc. Amer. Math. Soc.*137 (2009), no.6, 2057-2062. - On flows associated to Sobolev vector fields in Wiener spaces: an approach à la DiPerna-Lions (with L. Ambrosio)

*J. Funct. Anal.*256 (2009), no.1, 179-214. - On the Hausdorff Dimension of the Mather quotient (with A. Fathi and L. Rifford)

*Comm. Pure Appl. Math.*62 (2009), no. 4, 445-500. - A geometric lower bound on Grad's number

*ESAIM Control Optim. Calc. Var.*15 (2009), no. 3, 569-575. - Geodesics in the space of measure-preserving maps and plans (with L. Ambrosio)

*Arch. Ration. Mech. Anal.*194 (2009), no. 2, 421-462. - Generalized solutions for the Euler equations in one and two dimensions (with M. Bernot and F. Santambrogio)

*J. Math. Pures Appl.*91 (2008), no. 2, 137-155. - Convergence to the viscous porous medium equation and propagation of chaos (with R. Philipowski)

*ALEA Lat. Am. J. Probab. Math. Stat.*4 (2008), 185-203. - An approximation lemma about the cut locus, with applications in optimal transport theory (with C. Villani)

*Methods Appl. Anal.*15 (2008), no. 2, 149-154. - Absolute continuity of Wasserstein geodesics in the Heisenberg group (with N. Juillet)

*J. Funct. Anal.*255 (2008), no. 1, 133-141. - Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index (with A. Abbondandolo)

*J. Fixed Point Theory Appl.*3 (2008), no. 1, 95-120. - Synchronized traffic plans and stability of optima (with M. Bernot)

*ESAIM Control Optim. Calc. Var.*14 (2008), no. 4, 864-878. - A simple proof of the Morse-Sard theorem in Sobolev spaces

*Proc. Amer. Math. Soc.*136 (2008), no. 10, 3675-3681. - Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients

*J. Funct. Anal.*254 (2008), no. 1, 109-153. - On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations (with L. Ambrosio)

*Calc. Var. Partial Differential Equations*31 (2008), no. 4, 497-509. - Strong displacement convexity on Riemannian manifolds (with C. Villani)

*Math. Z.*257 (2007), no. 2, 251-259. - High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces (with A. Abbondandolo)

*J. Differential Equations*234 (2007), no. 2, 626-653. - Existence, uniqueness and regularity of optimal transport maps

*SIAM J. Math. Anal.*39 (2007), no. 1, 126-137. - The Monge problem on non-compact manifolds

*Rend. Sem. Mat. Univ. Padova*117 (2007), 147-166.