G. Alberti, L. Ambrosio, X. Cabré: On a long standing conjecture of E. De Giorgi: old and recent results Acta Appl. Math. Vol. 65 (2001), N. 1, p. 9-33, 2000 L. Ambrosio, X. Cabré: Entire Solutions of a Semilinear Elliptic Equation in ${\mathcal R}^3$ and a Conjecture of De Giorgi Journal of the AMS N. 13, p. 725-739, 2000 X. Cabré, E. Cinti: Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian Discrete Contin. Dyn. Syst. Vol. 28, N. 3, p. 1179--1206, 2010 X. Cabré, E. Cinti: Sharp energy estimates for nonlinear fractional diffusion equations Calc. Var. Partial Differential Equations (Accepted Paper) 2012 X. Cabré, E. Cinti, J. Serra: Stable $s$-minimal cones in $\mathbb R^3$ are flat for $s\sim 1$ J. Reine Angew. Math. (Crelle's Journal). (Accepted Paper) 2017 X. Cabré, G. Poggesi: Stable solutions to some elliptic problems: minimal cones, the Allen-Cahn equation, and blow-up solutions (preprint) 2018 X. Cabré, M. Cozzi, G. Csato: A fractional Michael-Simon Sobolev inequality on convex hypersurfaces (preprint) 2020 X. Cabré, A. Figalli, X. Ros-Oton, J. Serra: Stable solutions to semilinear elliptic equations are smooth up to dimension 9 Acta Mathematica 2020 X. Cabré, E. Cinti, J. Serra: Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime (Submitted Paper) 2021