General optimal transport theory

Published/accepted papers

  1. When is multidimensional screening a convex program? (with Y.-H. Kim and R. J. McCann)
    J. Econom. Theory 146 (2011), no. 2, 454-478.
  2. Local semiconvexity of Kantorovich potentials on non-compact manifolds (with N. Gigli)
    ESAIM Control Optim. Calc. Var. 17 (2011), no. 3, 648-653.
  3. Mass Transportation on Sub-Riemannian Manifolds (with L. Rifford)
    Geom. Funct. Anal. 20 (2010), no. 1, 124-159.
  4. The optimal partial transport problem
    Arch. Ration. Mech. Anal. 195 (2010), no. 2, 533-560.
  5. Optimal transportation on non-compact manifolds (with A. Fathi)
    Israel J. Math. 175 (2010), no. 1, 1-59.
  6. A note on the regularity of the free boundaries in the optimal partial transport problem
    Rend. Circ. Mat. Palermo 58 (2009), no. 2, 283-286.
  7. Absolute continuity of Wasserstein geodesics in the Heisenberg group (with N. Juillet)
    J. Funct. Anal. 255 (2008), no. 1, 133-141.
  8. Synchronized traffic plans and stability of optima (with M. Bernot)
    ESAIM Control Optim. Calc. Var. 14 (2008), no. 4, 864-878.
  9. Existence, uniqueness and regularity of optimal transport maps
    SIAM J. Math. Anal. 39 (2007), no. 1, 126-137.
  10. The Monge problem on non-compact manifolds
    Rend. Sem. Mat. Univ. Padova 117 (2007), 147-166.

Surveys and lecture notes

  1. An introduction to optimal transport and Wasserstein gradient flows
    Preprint 2023.
  2. Optimal Transport. Old and New. [book review]
    Bull. Amer. Math. Soc. (N.S.) 47 (2010), no. 4, 723-727.
  3. Optimal transport, Euler equations, Mather and DiPerna-Lions theories.
    Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009.