Quantitative logarithmic Sobolev inequalities and stability estimates (with M. Fathi and M. Ledoux)

Discrete Contin. Dyn. Syst., accepted (2015); arXiv.

A sharp lower bound on the polygonal isoperimetric deficit

Proc. Amer. Math. Soc., in press (2015); article; arXiv.

Regularity of shadows and the geometry of the singular set associated to a Monge-Ampere equation (with L. Nurbekyan)

Comm. Anal. Geom., to appear; arXiv.

Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems (with A. Minne)

Ann. Inst. H. Poincaré Anal. Non Linéaire, in press (2015); article; arXiv.

On the regularity of the free boundary in the optimal partial transport problem for general cost functions (with S. Chen)

J. Differential Equations, 258 (2015), no. 7, 2618-2632; article; arXiv.

On the stability of the polygonal isoperimetric inequality (with L. Nurbekyan)

Adv. Math., 276 (2015), 62-86; article; arXiv.

Obstructions to regularity in the classical Monge problem (with M. Colombo)

Math. Res. Lett., 21, no. 4, 2014; article; arXiv.

A quantitative log-Sobolev inequality for a two parameter family of functions (with D. Marcon)

Int. Math. Res. Not. IMRN, (2014) 2014 (20): 5563-5580; article; arXiv.

Free boundary regularity in the optimal partial transport problem

J. Funct. Anal., 264 (2013), no. 11, 2497-2528; article; arXiv.

A sharp stability result for the relative isoperimetric inequality inside convex cones (with A. Figalli) 

J. Geom. Anal., 23 (2013), no. 2, 938-969; article; arXiv. 

Preprints:

Non-transversal intersection of free and fixed boundary for fully nonlinear elliptic operators in two dimensions (with A. Minne) arXiv.