G. Acosta and R. G. Durán, An optimal poincaré inequality in L 1 for convex domains, Proceedings of the, pp.195-202, 2004.

H. Attouch, G. Buttazzo, and G. Michaille, Variational analysis in sobolev and bv spaces: applications to pdes and optimization, 2014.
DOI : 10.1137/1.9781611973488

F. Aurenhammer, F. Hoffmann, and B. Aronov, Minkowski-Type Theorems and Least-Squares Clustering, Algorithmica, vol.20, issue.1, pp.61-76, 1998.
DOI : 10.1007/PL00009187

J. Benamou, D. Brittany, . Froese, M. Adam, and . Oberman, Numerical solution of the Optimal Transportation problem using the Monge???Amp??re equation, Journal of Computational Physics, vol.260, pp.107-126, 2014.
DOI : 10.1016/j.jcp.2013.12.015

A. Luis and . Caffarelli, The regularity of mappings with a convex potential, J. Amer. Math. Soc, vol.592, issue.1, pp.99-104, 1992.

A. Luis, . Caffarelli, A. Sergey, . Kochengin, I. Vladimir et al., Problem of reflector design with given far-field scattering data, Monge Ampère Equation: Applications to Geometry and Optimization: NSF-CBMS Conference on the Monge Ampère Equation , Applications to Geometry and Optimization, p.13, 1997.

P. Machado-manhaes-de-castro, Q. Mérigot, and B. Thibert, Intersection of paraboloids and application to minkowski-type problems, Proceedings of the thirtieth annual symposium on Computational geometry, p.308, 2014.

K. Fernando-de-goes, V. Breeden, M. Ostromoukhov, and . Desbrun, Blue noise through optimal transport, ACM Transactions on Graphics (TOG), vol.31, issue.6, p.171, 2012.

C. Fernando-de-goes, J. Wallez, D. Huang, M. Pavlov, and . Desbrun, Power particles: an incompressible fluid solver based on power diagrams, ACM Transactions on Graphics (TOG), vol.34, issue.4, p.50, 2015.

A. Figalli, Y. Kim, and R. J. Mccann, H??lder Continuity and Injectivity of Optimal Maps, Archive for Rational Mechanics and Analysis, vol.12, issue.3, pp.747-795, 2013.
DOI : 10.1007/s00205-013-0629-5

S. Friedland and R. Nabben, On Cheeger-type inequalities for weighted graphs, Journal of Graph Theory, vol.103, issue.1, pp.1-17, 2002.
DOI : 10.1002/jgt.10037

N. Guillen and J. Kitagawa, On the local geometry of maps with c-convex potentials, Calculus of Variations and Partial Differential Equations, vol.255, issue.9, pp.345-387, 2015.
DOI : 10.1007/s00526-014-0715-z

A. S. Householder, The theory of matrices in numerical analysis, pp.51-14539, 1975.

D. Hug, Generalized curvature measures and singularities of sets with positive reach, Forum Mathematicum, vol.10, issue.6, pp.699-728, 1998.
DOI : 10.1515/form.10.6.699

Y. Kim and J. Kitagawa, On the Degeneracy of Optimal Transportation, Communications in Partial Differential Equations, vol.123, issue.7, pp.1329-1363, 2014.
DOI : 10.1016/j.jfa.2008.07.003

Y. Kim and R. J. Mccann, Continuity, curvature, and the general covariance of optimal transportation, Journal of the European Mathematical Society, vol.12, issue.4, pp.1009-1040, 2010.
DOI : 10.4171/JEMS/221

J. Kitagawa, An iterative scheme for solving the optimal transportation problem, Calculus of Variations and Partial Differential Equations, vol.20, issue.3, pp.243-263, 2014.
DOI : 10.1007/s00526-013-0673-x

B. Lévy, A numerical algorithm for L 2 semi-discrete optimal transport in 3d, ESAIM M2AN, vol.49, issue.6, 2015.

G. Loeper, On the regularity of solutions of optimal transportation problems Regularity of optimal maps on the sphere: the quadratic cost and the reflector antenna, Arch. Ration. Mech. Anal, vol.20, issue.199 1, pp.202-241, 2009.

G. Loeper and F. Rapetti, Numerical solution of the Monge???Amp??re equation by a Newton's algorithm, Comptes Rendus Mathematique, vol.340, issue.4, pp.319-324, 2005.
DOI : 10.1016/j.crma.2004.12.018

X. Ma, S. Neil, X. Trudinger, and . Wang, Regularity of potential functions of the optimal transportation problem, Archive for rational mechanics and analysis, pp.151-183, 2005.

Q. Mérigot, A Multiscale Approach to Optimal Transport, Computer Graphics Forum, vol.40, issue.2, pp.1583-1592, 2011.
DOI : 10.1111/j.1467-8659.2011.02032.x

J. Mirebeau, Discretization of the 3d monge-ampere operator, between wide stencils and power diagrams, arXiv preprint arXiv:1503, p.947, 2015.

V. Oliker and L. Prussner, On the numerical solution of the equation and its discretizations, pp.271-293, 1989.

L. Saumier, M. Agueh, and B. Khouider, An efficient numerical algorithm for the L2 optimal transport problem with periodic densities, IMA Journal of Applied Mathematics, vol.80, issue.1, pp.135-157, 2015.
DOI : 10.1093/imamat/hxt032

R. Schneider, Convex bodies: The brunn?minkowski theory, 1993.
DOI : 10.1017/CBO9780511526282

S. Neil, X. Trudinger, and . Wang, On the second boundary value problem for Monge- Ampère type equations and optimal transportation, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.8, issue.5 1, pp.143-174, 2009.

C. Villani, Optimal transport: old and new, 2009.
DOI : 10.1007/978-3-540-71050-9