Free Access
Volume 19, Number 3, July-September 2013
Page(s) 668 - 678
Published online 28 March 2013
  1. Y. Brenier, Decomposition polaire et rearrangement monotone des champs de vecteurs. C. R. Acad. Sci. Paris Ser. I Math. 305 (1987) 805–808. [MathSciNet] [Google Scholar]
  2. L.A. Caffarelli, The regularity of mappings with a convex potential. J. Amer. Math. Soc. 5 (1992) 99–104. [CrossRef] [MathSciNet] [Google Scholar]
  3. L.A. Caffarelli, Boundary regularity of maps with convex potentials. Comm. Pure Appl. Math. 45 (1992) 1141–1151. [CrossRef] [MathSciNet] [Google Scholar]
  4. L.A. Caffarelli, Boundary regularity of maps with convex potentials-II. Ann. of Math. 144 (1996) 453–496. [Google Scholar]
  5. L. Caffarelli, Allocation maps with general cost functions, in Partial Differential Equations and Applications, edited by P. Marcellini, G. Talenti and E. Vesintini. Lect. Notes Pure Appl. Math. 177 (1996) 29–35. [Google Scholar]
  6. G. Carlier and I. Ekeland, Matching for teams. Econ. Theory 42 (2010) 397–418. [CrossRef] [Google Scholar]
  7. P.-A. Chiappori, R. McCann and L. Nesheim, Hedonic price equilibria, stable matching and optimal transport, equivalence, topology and uniqueness. Econ. Theory 42 (2010) 317–354. [Google Scholar]
  8. P. Delanoë, Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampere operator. Ann. Inst. Henri Poincaré, Anal. Non Lineaire 8 (1991) 442–457. [Google Scholar]
  9. P. Delanoë, Gradient rearrangement for diffeomorphisms of a compact manifold. Differ. Geom. Appl. 20 (2004) 145–165. [CrossRef] [Google Scholar]
  10. P. Delanoë and Y. Ge, J. Reine Angew. Math. 646 (2010) 65–115. [MathSciNet] [Google Scholar]
  11. I. Ekeland, An optimal matching problem. ESAIM: COCV 11 (2005) 5771. [CrossRef] [EDP Sciences] [Google Scholar]
  12. I. Ekeland, Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types. Econ. Theory 42 (2010) 275–315. [Google Scholar]
  13. A. Figalli and L. Rifford, Continuity of optimal transport maps on small deformations of S2. Commun. Pure Appl. Math. 62 (2009) 1670–1706. [CrossRef] [Google Scholar]
  14. A. Figalli, Y.-H. Kim and R.J. McCann, When is multidimensional screening a convex program? J. Econ. Theory 146 (2011) 454–478. [CrossRef] [Google Scholar]
  15. A. Figalli, Y.-H. Kim and R.J. McCann, Höelder continuity and injectivity of optimal maps. Preprint available at [Google Scholar]
  16. A. Figalli, Y.-H. Kim and R.J. McCann, Regularity of optimal transport maps on multiple products of sphere. To appear in J. Eur. Math. Soc. Currently available at [Google Scholar]
  17. A. Figalli, L. Rifford and C. Villani, Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Tohoku Math. J. 63 (2011) 855–876. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Figalli, L. Rifford and C. Villani, Nearly round spheres look convex. Amer. J. Math. 134 (2012) 109–139. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Figalli, L. Rifford and C. Villani, On the Ma–Trudinger–Wang curvature on surfaces. Calc. Var. Partial Differ. Equ. 39 (2010) 307–332. [CrossRef] [Google Scholar]
  20. W. Gangbo, Habilitation thesis, Universite de Metz (1995). [Google Scholar]
  21. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [CrossRef] [MathSciNet] [Google Scholar]
  22. Y.-H. Kim, Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds. Int. Math. Res. Not. 2008 (2008) doi:10.1093/imrn/rnn120. [Google Scholar]
  23. Y.-H. Kim and R.J. McCann, Continuity, curvature and the general covariance of optimal transportation. J. Eur. Math. Soc. 12 (2010) 1009–1040. [Google Scholar]
  24. Y.-H. Kim and R.J. McCann, Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular). To appear in J. Reine Angew. Math. Currently available at [Google Scholar]
  25. V. Levin, Abstract cyclical monotonicity and Monge solutions for the general Monge-Kantorovich problem. Set-Val. Anal. 7 (1999) 7–32. [Google Scholar]
  26. J. Liu, Hölder regularity in optimal mappings in optimal transportation. To appear in Calc. Var. Partial Differ. Equ. [Google Scholar]
  27. G. Loeper, On the regularity of maps solutions of optimal transportation problems. Acta Math. 202 (2009) 241–283. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Loeper, Regularity of optimal maps on the sphere: The quadratic cost and the reflector antenna. Arch. Rational Mech. Anal. 199 (2011) 269–289. [CrossRef] [Google Scholar]
  29. G. Loeper and C. Villani, Regularity of optimal transport in curved geometry: the nonfocal case. Duke Math. J. 151 (2010) 431–485. [CrossRef] [MathSciNet] [Google Scholar]
  30. X.-N. Ma, N. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problem. Arch. Rational Mech. Anal. 177 (2005) 151–183. [Google Scholar]
  31. R.J. McCann, Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal. 11 (2001) 589–608. [CrossRef] [MathSciNet] [Google Scholar]
  32. R. McCann, B. Pass and M. Warren, Rectifiability of optimal transportation plans. Can. J. Math. 64 (2012) 924–933. [Google Scholar]
  33. B. Pass, Ph.D. thesis, University of Toronto (2011). [Google Scholar]
  34. B. Pass, Regularity of optimal transportation between spaces with different dimensions. Math. Res. Lett. 19 (2012) 291–307. [MathSciNet] [Google Scholar]
  35. N. Trudinger and X.-J. Wang, On the second boundary value problem for Monge-Ampere type equations and optimal transportation. Ann. Sc. Norm. Super. Pisa Cl. Sci. 8 (2009) 143–174. [MathSciNet] [Google Scholar]
  36. N. Trudinger and X.-J. Wang, On strict convexity and C1-regularity of potential functions in optimal transportation. Arch. Rational Mech. Anal. 192 (2009) 403–418. [CrossRef] [Google Scholar]
  37. J. Urbas, On the second boundary value problem for equations of Monge-Ampere type. J. Reine Angew. Math. 487 (1997) 115–124. [MathSciNet] [Google Scholar]
  38. C. Villani, Optimal transport: old and new, in Grundlehren der mathematischen Wissenschaften. Springer, New York 338 (2009). [Google Scholar]
  39. X.-J. Wang, On the design of a reflector antenna. Inverse Probl. 12 (1996) 351–375. [CrossRef] [MathSciNet] [Google Scholar]

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