# Selected papers

- 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)

*Preprint*
- 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.*, to appear
- Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)

*Duke Math. J.*, to appear
- 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.