An optimal poincaré inequality in L 1 for convex domains, Proceedings of the, pp.195-202, 2004. ,
Variational analysis in sobolev and bv spaces: applications to pdes and optimization, 2014. ,
DOI : 10.1137/1.9781611973488
Minkowski-Type Theorems and Least-Squares Clustering, Algorithmica, vol.20, issue.1, pp.61-76, 1998. ,
DOI : 10.1007/PL00009187
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
The regularity of mappings with a convex potential, J. Amer. Math. Soc, vol.592, issue.1, pp.99-104, 1992. ,
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. ,
Intersection of paraboloids and application to minkowski-type problems, Proceedings of the thirtieth annual symposium on Computational geometry, p.308, 2014. ,
Blue noise through optimal transport, ACM Transactions on Graphics (TOG), vol.31, issue.6, p.171, 2012. ,
Power particles: an incompressible fluid solver based on power diagrams, ACM Transactions on Graphics (TOG), vol.34, issue.4, p.50, 2015. ,
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
On Cheeger-type inequalities for weighted graphs, Journal of Graph Theory, vol.103, issue.1, pp.1-17, 2002. ,
DOI : 10.1002/jgt.10037
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
The theory of matrices in numerical analysis, pp.51-14539, 1975. ,
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
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
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
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
A numerical algorithm for L 2 semi-discrete optimal transport in 3d, ESAIM M2AN, vol.49, issue.6, 2015. ,
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. ,
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
Regularity of potential functions of the optimal transportation problem, Archive for rational mechanics and analysis, pp.151-183, 2005. ,
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
Discretization of the 3d monge-ampere operator, between wide stencils and power diagrams, arXiv preprint arXiv:1503, p.947, 2015. ,
On the numerical solution of the equation and its discretizations, pp.271-293, 1989. ,
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
Convex bodies: The brunn?minkowski theory, 1993. ,
DOI : 10.1017/CBO9780511526282
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. ,
Optimal transport: old and new, 2009. ,
DOI : 10.1007/978-3-540-71050-9