Articles et preprints

• Interpolation, convexity and geometric inequalities, preprint (2011). (with B. Klartag)
  
• Invariances in variance estimates, preprint (2011), to appear in Journal of the London Math. Soc. (with F. Barthe).
• Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures, preprint (2011), to appear in Ann. Inst. H. Poincaré Probab. Statist. (with E. Carlen and E. Lieb).
  
• Hypercontractive measures, Talagrand's inequality and influences, preprint (2011), to appear in Geometric Aspects of Functional Analysis. (with M. Ledoux).
• Correlation and Brascamp-Lieb inequalities for Markov semigroups, Int. Math. Res. Notices 2011 No. 10 (2011), 2177–2216. (with. F. Barthe, M. Ledoux and B. Maurey). Link to pdf file. (If it doesn't work, then click here).
• The geometry of Euclidean convolution inequalities and entropy, Proc. A. M. S. 138 (2010) no. 8, 2755–2769. (with M. Ledoux).
• Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities, Geom. Funct. Anal. 19 (2009) 373-405. (with E. Carlen).
• Entropy of spherical marginals and related inequalities, J. Math. Pures Appl. (9)  86  (2006), no. 2, 89-99. (with F. Barthe and B. Maurey).
• Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields and optimal transport, Ann. Fac. Sci. Toulouse Math. (6)  15  (2006), no. 4, 613-635. (with R.J. McCann and M. Schmuckenschläger).
• On Berndtsson's generalization of Prékopa's theorem, Math. Z. 249 (2005), no. 2, 401-410.
• The (B)-conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems, J. Funct. Anal. 214 (2004), 410-427. (with M. Fradelizi and B. Maurey).
• Inverse Brascamp-Lieb inequalities along the Heat equation, in Geometric Aspects of Functional Analysis (2002-2003), LNM 1850, Springer, 2004, pp. 65-71. (with F. Barthe).
• Inequalities for generalized entropy and optimal transportation, in Recent Advances in the Theory and Applications of Mass Transport, Contemp. Math. 353, A.M.S., Providence, R.I., 2004. (with C. Houdré and W. Gangbo).
• Non-smooth differential properties of optimal transport, in in Recent Advances in the Theory and Applications of Mass Transport, Contemp. Math. 353, A.M.S., Providence, R.I., 2004.
• A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities, Advances in Math. 182 (2004) 307-332. (with B. Nazaret and C. Villani).
• Santalo's inequality on C^n by complex interpolation, C.R. Acad. Sci. Paris Sér. I Math. 334 (2002), 767-772.
• Some applications of mass transport to Gaussian type inequalities, Arch. Rational Mech. Anal. 161 (2002), 257-269.
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb, Invent. Math. 146 (2001), 219--257. (with R.J. McCann and M. Schmuckenschläger).
• Gaussian shift inequalities and norms of barycenters, Studia Math. 146 (2001), 245--259. (with F. Barthe and M. Fradelizi).
• Inégalité de Prékopa-Leindler sur la sphère, C.R. Acad. Sci. Paris Sér. I Math. 329 (1999), 789-792.
• Sur le transport de mesures périodiques, C.R. Acad. Sci. Paris Sér. I Math. 329 (1999), 199--202.

Surveys

• Convexité, log-concavité et inégalités à la Brunn-Minkowski. Aspects géométriques, fonctionnels et probabilistes. Synthèse des travaux de l'HDR, décembre 2006 (64 pages).
• Quelques exemples d'application du transport de mesure en géométrie euclidienne et riemannienne, Séminaire de théorie spectrale et géométrie, Grenoble, volume 22 (2004), 125--152.