P. Appell, Mémoire sur les déblais et remblais des systèmes continus ou discontinus, Mémoires Acad. Sci. Inst. France Paris, vol.29, pp.1-208, 1887.

T. Aubin, Nonlinear Analysis on Manifolds. Monge?Ampère equations, Grund. math. Wiss, 1982.

A. Banyaga, Formes volume sur les variétésvariétésà bord, Enseignement Math, pp.127-131, 1974.

Y. Brenier, U. Frisch, M. Hénon, G. Loeper, S. Matarrese et al., Sobolevski? ?, Reconstruction of the early Universe as a convex optimization problem, Mon. Not. R. Astron. Soc, pp.346-501, 2003.

L. A. Caffarelli, Allocation maps with general cost functions Partial Differential Equations and Applications: collected papers in honor of Carlo Pucci, Lecture Notes in Pure and Appl. Math. 177, pp.29-35, 1996.

B. Dacorogna and J. Moser, On a partial differential equation involving the Jacobian determinant, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.7, issue.1, pp.1-26, 1990.
DOI : 10.1016/S0294-1449(16)30307-9

. Ph and . Delanoë, Variational heuristics for optimal transportation maps on compact manifolds, Analysis, vol.29, pp.221-228, 2009.

D. G. Ebin and J. Marsden, Groups of Diffeomorphisms and the Motion of an Incompressible Fluid, The Annals of Mathematics, vol.92, issue.1, pp.102-163, 1970.
DOI : 10.2307/1970699

L. C. Evans, Partial Differential Equations and Monge-Kantorovich Mass Transfer, Current Developments in Mathematics, vol.1997, issue.1, pp.65-126, 1997.
DOI : 10.4310/CDM.1997.v1997.n1.a2

W. Gangbo and R. J. Mccann, The geometry of optimal transportation, Acta Mathematica, vol.177, issue.2, pp.113-161, 1996.
DOI : 10.1007/BF02392620

N. Guillen and R. J. Mccann, Five lectures on optimal transportation: geometry, regularity and applications, Preprint, 2010.

Y. , ?. H. Kim, and R. J. Mccann, Continuity, curvature, and the general covariance of optimal transportation, J. Eur. Math. Soc, vol.12, pp.1009-1040, 2010.

R. J. Mccann, Polar factorization of maps on Riemannian manifolds, Geometric and Functional Analysis, vol.11, issue.3, pp.589-608, 2001.
DOI : 10.1007/PL00001679

G. Monge, Mémoire sur la théorie des déblais et remblais, Mémoires Acad, Royale Sci. Paris, 1781.

J. Moser, On the volume elements on a manifold, Transactions of the American Mathematical Society, vol.120, issue.2, pp.286-294, 1965.
DOI : 10.1090/S0002-9947-1965-0182927-5

N. S. Trudinger, Optimal transportation and nonlinear partial differential equations (slides), 26th Brazilian Mathematical Colloquium, 2007.

J. Urbas, Mass transfer problems, Univ, Bonn Lecture Notes, 1998.

C. Villani, Optimal Transport, Old and New, Grund. math. Wiss, 2009.