Papers and preprints

• Duality and Heat flow, preprint 2024 (with N. Gozlan, S. Nakamura and S. Tsjui).
• Discrete logarithmic Sobolev inequalities in Banach spaces, to appear in J. London Math. Soc. (with A. Eskenazis)
• A Gaussian correlation inequality for p.s.h. functions, to appear in Ann. IHP Proba. (with F. Barthe)
• Improved log-concavity for rotationally invariant measures of symmetric convex sets, Annals of Prob. (2023) 51, 987–1003 (with L. Rotem).
• Talagrand’s influence inequality revisited, Analysis & PDE 16 (2023), pp. 571–612 DOI: 10.2140/apde.2023.16.571(with A. Eskenazis).
• New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality, I.M.R.N. 2020 (2020), 3042–3083. (with F. Bolley, Y. Fujita, A. Guillin and I. Gentil).
• One more proof of the Alexandrov-Fenchel inequalities, C. R. Math. Acad. Sci. Paris 357 (2019), 676–680. (with B. Klartag, Q. Merigot and F. Santambrogio).
• Regularity of monotone maps between unbounded domains, Discrete & Contin. Dyn. Syst. 39 (2019), 7101–7112. (with A. Figalli).
• On matrix-valued and log-concavity and related Prékopa and Brascamp-Lieb inequalities, Advances in Math. 351 (2019), 96–116.
• Complex Legendre duality, Amer. J. of Math. 142 (2020), 323–339. (with B. Berndtsson, B. Klartag and Y. Rubinstein).
• Complex interpolation of R-norms, duality and foliations, J. Eur. Math. Soc 22 (2020), 477–505 (with B. Berndtsson, B. Klartag and Y. Rubinstein).
• Several results regarding the (B)-conjecture, in Geometric Aspects of Functional Analysis (Gafa seminar) LNM vol 2256, Springer, 2020. (with L. Rotem).
• Transport inequalities for log-concave measures, quantitative forms and applications, Canadian J. of Math. 69 (2017), 481-501.
• Some extensions of the Prékopa-Leindler inequality using Borell’s stochastic approach, Studia Math. 238 (2017), 201-233. (with B. Maurey).
• Volume of the polar of random sets and shadow systems, Math. Annalen 362 (2015), 1305-1325. (with M. Fradelizi G. Paouris and P. Pivovarov).
• Moment measure, J. Funct. Anal. 268 (2015) 3834-3866. (with B. Klartag).
• Transport proofs of weighted Poincaré inequalities for log-concave distributions, Bernoulli - to appear (2015). (with N. Gozlan)
• KLS-type isoperimetric bounds for log-concave probability measures, Annali di Matematica Pura ed Applicata.
• A transport inequality on the sphere obtained by mass transport,Pacific Journal of Mathematics, Vol. 268 (2014), No. 1, 23-31.
• Invariances in variance estimates, Proc. London Math. Soc. 106 (2013) 33-64. (with F. Barthe).
• Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures, Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), 1-12. (with E. Carlen and E. Lieb).
• Interpolation, convexity and geometric inequalities, in Geometric Aspects of Functional Analysis, LNM 2050, Springer, 2012, pp 151-168 (with B. Klartag)
• Hypercontractive measures, Talagrand’s inequality and influences, in Geometric Aspects of Functional Analysis, LNM 2050, Springer, 2012, pp 169-189. (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).
• 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) (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. (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 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.

Autre

• 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.