Optimal transport and Riemannian geometry

Published/accepted papers

8. On the convexity of injectivity domains on nonfocal manifolds (with T. Gallouët and L. Rifford)
   SIAM J. Math. Anal. 47 (2015), no. 2, 969-1000.
9. Nearly round spheres look convex (with L. Rifford and C. Villani)
   Amer. J. Math. 134 (2012), no. 1, 109-139.
10. Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds (with L. Rifford and C. Villani)
    Tohoku Math. J. (2) 63 (2011), no. 4, 855-876.
11. Tangent cut loci on surfaces (with L. Rifford and C. Villani)
    Differential Geom. Appl. 29 (2011), no. 2, 154-159.
12. On the Ma-Trudinger-Wang curvature on surfaces (with L. Rifford and C. Villani)
    Calc. Var. Partial Differential Equations 39 (2010), no. 3, 307-332.
13. Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S² (with L. Rifford)
    Comm. Pure Appl. Math. 62 (2009), no. 12, 1670-1706.
14. An approximation lemma about the cut locus, with applications in optimal transport theory (with C. Villani)
    Methods Appl. Anal. 15 (2008), no. 2, 149-154.
15. Strong displacement convexity on Riemannian manifolds (with C. Villani)
    Math. Z. 257 (2007), no. 2, 251-259.

Surveys and lecture notes

2. Optimal Transport and Curvature (with C. Villani)
   Nonlinear PDE's and applications, 171-217, Lecture Notes in Math. 2028, Springer, Heidelberg, 2011.
3. Optimal transport, Euler equations, Mather and DiPerna-Lions theories.
   Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009.