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Volumn 177, Issue 2, 1996, Pages 113-161

The geometry of optimal transportation

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EID: 0001103156     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02392620     Document Type: Article
Times cited : (723)

References (43)
  • 1
    • 0009252869 scopus 로고
    • Détermination d'un couple optimal du problème de Monge-Kantorovitch
    • ABDELLAOUI, T., Détermination d'un couple optimal du problème de Monge-Kantorovitch. C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), 981-984.
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.319 , pp. 981-984
    • Abdellaoui, T.1
  • 3
    • 0002967985 scopus 로고
    • On the structure of singular sets of convex functions
    • ALBERTI, G., On the structure of singular sets of convex functions. Calc. Var. Partial Differential Equations, 2 (1994), 17-27.
    • (1994) Calc. Var. Partial Differential Equations , vol.2 , pp. 17-27
    • Alberti, G.1
  • 4
    • 0037820063 scopus 로고
    • Existence and uniqueness of a convex surface with a given integral curvature
    • ALEKSANDROV, A. D., Existence and uniqueness of a convex surface with a given integral curvature. C. R. (Doklady) Acad. Sci. URSS (N. S.), 35 (1942), 131-134.
    • (1942) C. R. (Doklady) Acad. Sci. URSS (N. S.) , vol.35 , pp. 131-134
    • Aleksandrov, A.D.1
  • 6
    • 0000741430 scopus 로고
    • An extension of duality-stability relations to non-convex optimization problems
    • BALDER, E. J., An extension of duality-stability relations to non-convex optimization problems. SIAM J. Control Optim., 15 (1977), 329-343.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 329-343
    • Balder, E.J.1
  • 7
    • 0001016311 scopus 로고
    • Décomposition polaire et réarrangement monotone des champs de vecteurs
    • BRENIER, Y., Décomposition polaire et réarrangement monotone des champs de vecteurs. C. R. Acad. Sci. Paris Sér. I Math., 305 (1987), 805-808.
    • (1987) C. R. Acad. Sci. Paris Sér. I Math. , vol.305 , pp. 805-808
    • Brenier, Y.1
  • 8
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • _ Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl Math., 44 (1991), 375-417.
    • (1991) Comm. Pure Appl Math. , vol.44 , pp. 375-417
  • 9
    • 84968482174 scopus 로고
    • The regularity of mappings with a convex potential
    • CAFFARELLI, L., The regularity of mappings with a convex potential. J. Amer. Math. Soc., 5 (1992), 99-104.
    • (1992) J. Amer. Math. Soc. , vol.5 , pp. 99-104
    • Caffarelli, L.1
  • 10
    • 0002669187 scopus 로고    scopus 로고
    • Allocation maps with general cost functions
    • Partial Differential Equations and Applications (P. Marcellini, G. Talenti and E. Vesintini, eds.). Dekker, New York
    • _ Allocation maps with general cost functions, in Partial Differential Equations and Applications (P. Marcellini, G. Talenti and E. Vesintini, eds.). pp. 29-35. Lecture Notes in Pure and Appl. Math., 177. Dekker, New York, 1996.
    • (1996) Lecture Notes in Pure and Appl. Math. , vol.177 , pp. 29-35
  • 11
    • 0000314501 scopus 로고
    • Notes on the Wasserstein metric in Hilbert spaces
    • CUESTA-ALBERTOS, J. A. & MATRÁN, C., Notes on the Wasserstein metric in Hilbert spaces. Ann. Probab., 17 (1989), 1264-1276.
    • (1989) Ann. Probab. , vol.17 , pp. 1264-1276
    • Cuesta-Albertos, J.A.1    Matrán, C.2
  • 14
    • 38249005078 scopus 로고
    • A characterization for the solution of the Monge-Kantorovich mass transference problem
    • CUESTA-ALBERTOS, J. A. & TUERO-DÍAZ, A., A characterization for the solution of the Monge-Kantorovich mass transference problem. Statist. Probab. Lett., 16 (1993), 147-152.
    • (1993) Statist. Probab. Lett. , vol.16 , pp. 147-152
    • Cuesta-Albertos, J.A.1    Tuero-Díaz, A.2
  • 15
    • 0002630652 scopus 로고
    • Sugli estremi dei momenti delle funzioni di ripartizione-doppia
    • DALL'AGLIO, G., Sugli estremi dei momenti delle funzioni di ripartizione-doppia. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 10 (1956), 35-74.
    • (1956) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) , vol.10 , pp. 35-74
    • Dall'Aglio, G.1
  • 16
    • 0038849266 scopus 로고
    • Prix bordin (géométrie)
    • DARBOUX, G., Prix Bordin (géométrie). C. R. Acad. Sci. Paris, 101 (1885), 1312-1316.
    • (1885) C. R. Acad. Sci. Paris , vol.101 , pp. 1312-1316
    • Darboux, G.1
  • 17
    • 0005785170 scopus 로고
    • Solutions in the large for multi-dimensional non-linear partial differential equations of first order
    • DOUGLIS, A., Solutions in the large for multi-dimensional non-linear partial differential equations of first order. Ann. Inst. Fourier (Grenoble), 15:2 (1965), 1-35.
    • (1965) Ann. Inst. Fourier (Grenoble) , vol.15 , Issue.2 , pp. 1-35
    • Douglis, A.1
  • 19
    • 0001309929 scopus 로고
    • Sur la distance de deux lois de probabilité
    • FRÉCHET, M., Sur la distance de deux lois de probabilité. C. R. Acad. Sci. Paris, 244 (1957), 689-692.
    • (1957) C. R. Acad. Sci. Paris , vol.244 , pp. 689-692
    • Fréchet, M.1
  • 22
    • 0001010507 scopus 로고
    • On a problem of Monge
    • in Russian
    • _ On a problem of Monge. Uspekhi Mat Nauk., 3 (1948), 225-226 (in Russian).
    • (1948) Uspekhi Mat Nauk. , vol.3 , pp. 225-226
  • 24
    • 0000485730 scopus 로고
    • Duality theorems for marginal problems
    • KELLERER, H. G., Duality theorems for marginal problems. Z. Wahrsch. Verw. Gebiete, 67 (1984), 399-432.
    • (1984) Z. Wahrsch. Verw. Gebiete , vol.67 , pp. 399-432
    • Kellerer, H.G.1
  • 25
    • 0021421774 scopus 로고
    • On the optimal mapping of distributions
    • KNOTT, M. & SMITH, C. S., On the optimal mapping of distributions. J. Optim. Theory Appl., 43 (1984), 39-49.
    • (1984) J. Optim. Theory Appl. , vol.43 , pp. 39-49
    • Knott, M.1    Smith, C.S.2
  • 26
    • 0002345026 scopus 로고
    • General Monge-Kantorovich problem and its applications in measure theory and mathematical economics
    • L. J. Leifmari, ed., Oxford Univ. Press, New York
    • LEVIN, V. L., General Monge-Kantorovich problem and its applications in measure theory and mathematical economics, in Functional Analysis, Optimization, and Mathematical Economics (L. J. Leifmari, ed.), pp. 141-176. Oxford Univ. Press, New York, 1990.
    • (1990) Functional Analysis, Optimization, and Mathematical Economics , pp. 141-176
    • Levin, V.L.1
  • 27
    • 84974004014 scopus 로고
    • Existence and uniqueness of monotone measure-preserving maps
    • MCCANN, R. J., Existence and uniqueness of monotone measure-preserving maps. Duke Math. J., 80 (1995), 309-323.
    • (1995) Duke Math. J. , vol.80 , pp. 309-323
    • McCann, R.J.1
  • 28
    • 85033762084 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • To appear
    • _ A convexity principle for interacting gases. To appear in Adv. in Math.
    • Adv. in Math.
  • 31
    • 0001662944 scopus 로고
    • The Monge-Kantorovich mass transference problem and its stochastic applications
    • RACHEV, S. T., The Monge-Kantorovich mass transference problem and its stochastic applications. Theory Probab. Appl., 29 (1984), 647-676.
    • (1984) Theory Probab. Appl. , vol.29 , pp. 647-676
    • Rachev, S.T.1
  • 32
    • 84972545670 scopus 로고
    • Characterization of the subdifferentials of convex functions
    • ROCKAFELLAR, R. T., Characterization of the subdifferentials of convex functions. Pacific J. Math., 17 (1966), 497-510.
    • (1966) Pacific J. Math. , vol.17 , pp. 497-510
    • Rockafellar, R.T.1
  • 33
    • 0004267646 scopus 로고
    • Princeton Univ. Press, Princeton, NJ
    • _ Convex Analysis. Princeton Univ. Press, Princeton, NJ, 1972.
    • (1972) Convex Analysis
  • 34
    • 0038849263 scopus 로고
    • Bounds for distributions with multivariate marginals
    • K. Mosler and M. Scarsini, eds., IMS Lecture Notes - Monograph Series. Inst. of Math. Statist., Hayward, CA
    • RÜSCHENDORF, L., Bounds for distributions with multivariate marginals, in Stochastic Orders and Decision Under Risk (K. Mosler and M. Scarsini, eds.), pp. 285-310. IMS Lecture Notes - Monograph Series. Inst. of Math. Statist., Hayward, CA, 1991.
    • (1991) Stochastic Orders and Decision Under Risk , pp. 285-310
    • Rüschendorf, L.1
  • 35
    • 0002558803 scopus 로고
    • Fréchet bounds and their applications
    • G. Dall'Aglio et al., Math. Appl., Kluwer Acad. Publ., Dordrecht
    • _ Fréchet bounds and their applications, in Advances in Probability Distributions with Given Marginals (G. Dall'Aglio et al., eds.), pp. 151-187. Math. Appl., 67. Kluwer Acad. Publ., Dordrecht, 1991.
    • (1991) Advances in Probability Distributions with Given Marginals , vol.67 , pp. 151-187
  • 36
    • 0001114165 scopus 로고
    • Optimal solutions of multivariate coupling problems
    • _ Optimal solutions of multivariate coupling problems. Appl. Math. (Warszaw), 23 (1995), 325-338.
    • (1995) Appl. Math. (Warszaw) , vol.23 , pp. 325-338
  • 37
    • 0030584978 scopus 로고    scopus 로고
    • On c-optimal random variables
    • _ On c-optimal random variables. Statist. Probab. Lett., 27 (1996), 267-270.
    • (1996) Statist. Probab. Lett. , vol.27 , pp. 267-270
  • 40
    • 0023291797 scopus 로고
    • On the optimal transportation of distributions
    • SMITH, C. & KNOTT, M., On the optimal transportation of distributions. J. Optim. Theory Appl., 52 (1987), 323-329.
    • (1987) J. Optim. Theory Appl. , vol.52 , pp. 323-329
    • Smith, C.1
  • 41
    • 0000012825 scopus 로고
    • On Hoeffding-Fréchet bounds and cyclic monotone relations
    • _ On Hoeffding-Fréchet bounds and cyclic monotone relations. J. Multivariate Anal., 40 (1992), 328-334.
    • (1992) J. Multivariate Anal. , vol.40 , pp. 328-334
  • 42
    • 0003299763 scopus 로고
    • Geometric problems in the theory of infinite-dimensional probability distributions
    • SUDAKOV, V. N., Geometric problems in the theory of infinite-dimensional probability distributions. Proc. Steklov Inst. Math., 141 (1979), 1-178.
    • (1979) Proc. Steklov Inst. Math. , vol.141 , pp. 1-178
    • Sudakov, V.N.1
  • 43
    • 0000884525 scopus 로고
    • On the differentiation of convex functions in finite and infinite dimensional spaces
    • ZAJÍČEK, L., On the differentiation of convex functions in finite and infinite dimensional spaces. Czechoslovak Math. J., 29 (104) (1979), 340-348.
    • (1979) Czechoslovak Math. J. , vol.29 , Issue.104 , pp. 340-348
    • Zajíček, L.1


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