Functional and geometric inequalities
- Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)
Duke Math. J. 171 (2022), no. 12, 2407–2459.
- Strong stability for the Wulff inequality with a crystalline norm (with Y. Ru-Ya Zhang)
Comm. Pure Appl. Math. 75 (2022), no. 2, 422–446.
- A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces (with D. Jerison)
Ann. Sci. Éc. Norm. Supér., to appear
- 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 sharp stability of critical points of the Sobolev inequality (with F. Glaudo)
Arch. Ration. Mech. Anal. 237 (2020), no. 1, 201–258.
- 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.
- The sharp quantitative Euclidean concentration inequality (with F. Maggi and C. Mooney)
Camb. J. Math. 6 (2018), no. 1, 59-87.
- Gradient stability for the Sobolev inequality: the case p≥2 (with R. Neumayer)
J. Eur. Math. Soc. (JEMS) 21 (2019), no. 2, 319-354.
- Quantitative stability for the Brunn-Minkowski inequality (with D. Jerison)
Adv. Math. 314 (2017), 1-47.
- 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.
- Quantitative stability for sumsets in Rn (with D. Jerison)
J. Eur. Math. Soc. (JEMS) 17 (2015), no. 5, 1079-1106.
- 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 the isoperimetric problem for radial log-convex densities (with F. Maggi)
Calc. Var. Partial Differential Equations 48 (2013), no. 3-4, 447-489.
- 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.
- A sharp stability result for the relative isoperimetric inequality inside convex cones (with E. Indrei)
J. Geom. Anal. 23 (2013), no. 2, 938-969.
- Isoperimetric-type inequalities on constant curvature manifolds (with Y. Ge)
Adv. Calc. Var. 5 (2012), no. 3, 251-284.
- A mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
Invent. Math. 182 (2010), no. 1, 167-211.
- 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.
- A note on Cheeger sets (with F. Maggi and A. Pratelli)
Proc. Amer. Math. Soc. 137 (2009), no.6, 2057-2062.
- A geometric lower bound on Grad's number
ESAIM Control Optim. Calc. Var. 15 (2009), no. 3, 569-575.
- Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (with J. Dolbeault, M. J. Esteban, R. L. Frank, M. Loss)
- A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions (with K. J. Böröczky and J. P. G. Ramos)
Surveys and lecture notes
- Stability results for the Brunn-Minkowski inequality
Colloquium De Giorgi 2013 and 2014, 119-127, Colloquia 5, Ed. Norm., Pisa, 2014.
- Quantitative stability results for the Brunn-Minkowski inequality
Proceedings of the ICM 2014.
- Stability in geometric and functional inequalities
Proceedings of the 6th European Congress of Mathematics, 2012.
- Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals
Concentration, functional inequalities and isoperimetry, 77-87, Contemp. Math. 545, Amer. Math. Soc., Providence, RI, 2011.
- Optimal transport, Euler equations, Mather and DiPerna-Lions theories.
Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009.