# Selected papers

- Sharp quantitative stability of the Brunn-Minkowski inequality (with P. van Hintum and M. Tiba)

*Preprint* - Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (with J. Dolbeault, M. J. Esteban, R. L. Frank, M. Loss)

*Preprint* - Complete classification of global solutions to the obstacle problem (with S. Eberle and G.S. Weiss)

*Preprint* - The singular set in the Stefan problem (with X. Ros-Oton and J. Serra)

*J. Amer. Math. Soc.*, to appear - Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 (with A. Belotto da Silva, A. Parusiński and L. Rifford)

*Invent. Math.*229 (2022), no. 1, 395–448. - Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)

*Duke Math. J.*171 (2022), no. 12, 2407–2459. - 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. - 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. - On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)
*Invent. Math.*, 215 (2019), no. 1, 311-366. - 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. - Universality in several-matrix models via approximate transport maps (with A. Guionnet)
*Acta Math.*217 (2016), no. 1, 81-176. - Partial regularity for optimal transport maps (with G. De Philippis)

*Publ. Math. Inst. Hautes Études Sci.*121 (2015), 81-112. - Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)

*Invent. Math.*200 (2015), no. 1, 201-261. - 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. - W
^{2,1}regularity for solutions of the Monge-Ampère equation (with G. De Philippis)

*Invent. Math.*192 (2013), no. 1, 55-69. - 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 mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
*Invent. Math.*182 (2010), no. 1, 167-211.