Selected Papers

Below is a selection of my papers. For the complete lists, see Published and accepted papers and Submitted papers and preprints.

22. Stable solutions of the Allen–Cahn equation in dimension three are one-dimensional (with H. Chan, X. Fernández-Real, E. Florit-Simon, and J. Serra)
    Preprint, 2026.
23. The generic structure of the singular set in the Stefan problem (with G. Colombo)
    Preprint, 2026.
24. Global regularity and free boundary geometry in the planar Rochet-Choné model (with S. Chen and Y. Ru-Ya Zhang)
    Preprint, 2026.
25. Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities (with P. van Hintum and M. Tiba)
    Preprint, 2026.
26. Global stable solutions to the free boundary Allen–Cahn and Bernoulli problems in 3D are one-dimensional (with H. Chan, X. Fernández-Real, and J. Serra)
    J. Amer. Math. Soc., 39 (2026), no. 4, 1027-1151.
27. Stable semilinear elliptic equations: $\varepsilon$-regularity à la Brezis and dimensional bounds for the singular set (with F. Franceschini)
    Preprint, 2026.
28. Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (with J. Dolbeault, M. J. Esteban, R. L. Frank, and M. Loss)
    Camb. J. Math., 13 (2025), no. 2, 359–430.
29. Sharp quantitative stability of the Brunn-Minkowski inequality (with P. van Hintum and M. Tiba)
    Preprint, 2025.
30. Complete classification of global solutions to the obstacle problem (with S. Eberle and G.S. Weiss)
    Ann. of Math., (2) 201 (2025), no. 1, 167–224.
31. The singular set in the Stefan problem (with X. Ros-Oton and J. Serra)
    J. Amer. Math. Soc. 37 (2024), no. 2, 305–389.
32. Constraint maps: singularities vs free boundaries (with A. Guerra, S. Kim, and H. Shahgholian)
    Preprint, 2024.
33. Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)
    Duke Math. J. 171 (2022), no. 12, 2407–2459.
34. 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.
35. 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.
36. 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.
37. 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.
38. On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)
    Invent. Math. 215 (2019), no. 1, 311-366.
39. Universality in several-matrix models via approximate transport maps (with A. Guionnet)
    Acta Math. 217 (2016), no. 1, 81-176.
40. Partial regularity for optimal transport maps (with G. De Philippis)
    Publ. Math. Inst. Hautes Études Sci. 121 (2015), 81-112.
41. Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)
    Invent. Math. 200 (2015), no. 1, 201-261.
42. $W^{2,1}$ regularity for solutions of the Monge-Ampère equation (with G. De Philippis)
    Invent. Math. 192 (2013), no. 1, 55-69.
43. A mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
    Invent. Math. 182 (2010), no. 1, 167-211.