Задача Монжа - Канторовича: достижения, связи и перспективы@@@The Monge - Kantorovich problem: achievements, connections, and perspectives
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Владимир Игоревич Богачев | Vladimir I. Bogachev | Александр Викторович Колесников | Aleksandr Viktorovich Kolesnikov
[1] R. McCann,et al. Free boundaries in optimal transport and Monge-Ampere obstacle problems , 2010 .
[2] Solution of the Monge–Ampère equation on Wiener space for general log-concave measures , 2006 .
[3] J. Rodrigues,et al. Recent Advances in the Theory and Applications of Mass Transport , 2004 .
[4] Karl-Theodor Sturm,et al. Entropic Measure and Wasserstein Diffusion , 2007, 0704.0704.
[5] Y. Brenier. Polar Factorization and Monotone Rearrangement of Vector-Valued Functions , 1991 .
[6] L. Ambrosio. Lecture Notes on Optimal Transport Problems , 2003 .
[7] A Note on the Equality in the Monge and Kantorovich Problems , 2006 .
[8] R. Arens,et al. On embedding uniform and topological spaces. , 1956 .
[9] C. Villani,et al. Ricci curvature for metric-measure spaces via optimal transport , 2004, math/0412127.
[10] Анатолий Моисеевич Вершик,et al. Универсальное пространство Урысона, метрические тройки Громова и случайные метрики на натуральном ряде@@@The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers , 1998 .
[11] R. McCann,et al. Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs , 2001 .
[12] L. Pascale,et al. Minimal measures, one-dimensional currents and the Monge–Kantorovich problem , 2006 .
[13] On displacement interpolation of measures involved in Brenier’s theorem , 2011 .
[14] A. Figalli. The Optimal Partial Transport Problem , 2010 .
[15] S. Bobkov. Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures , 1999 .
[16] Точные решения одномерной задачи Монжа - Канторовича@@@Precise solutions of the one-dimensional Monge - Kantorovich problem , 2004 .
[17] L. Rüschendorf,et al. A general duality theorem for marginal problems , 1995 .
[18] A. Figalli,et al. Optimal transportation on non-compact manifolds , 2007, 0711.4519.
[19] R. McCann. A Convexity Principle for Interacting Gases , 1997 .
[20] Nestor Guillen,et al. Five lectures on optimal transportation: Geometry, regularity and applications , 2010, 1011.2911.
[21] P. Castillon. Submanifolds, isoperimetric inequalities and optimal transportation , 2009, 0908.2711.
[22] J. Carrillo,et al. Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations , 2011 .
[23] V. Bogachev,et al. Triangular transformations of measures , 2005 .
[24] F. Barthe,et al. Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry , 2004, math/0407219.
[25] Замечание о равенстве в задачах Монжа и Канторовича@@@A remark on the equality in Monge and Kantorovich problems , 2005 .
[27] A. Üstünel,et al. The Notion of Convexity and Concavity on Wiener Space , 2000, 0809.0812.
[28] I. Fragalà,et al. Continuity of an optimal transport in Monge problem , 2005 .
[29] N. Trudinger,et al. The Monge-Ampµere equation and its geometric applications , 2008 .
[30] Felix Otto,et al. Eulerian Calculus for the Contraction in the Wasserstein Distance , 2005, SIAM J. Math. Anal..
[31] D. Kinderlehrer,et al. THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .
[32] Balls have the worst best Sobolev inequalities. Part II: variants and extensions , 2007 .
[33] W. Schachermayer,et al. Duality for Borel measurable cost functions , 2008, 0807.1468.
[34] A. Vershik. Some remarks on the infinite-dimensional problems of linear programming , 1970 .
[35] J. Moser. On the volume elements on a manifold , 1965 .
[36] Steven Haker,et al. Minimizing Flows for the Monge-Kantorovich Problem , 2003, SIAM J. Math. Anal..
[37] Karl-Theodor Sturm,et al. Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces , 2010, 1003.2116.
[38] E. Milman. Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower Bound , 2009, 0902.1560.
[39] R. McCann. Polar factorization of maps on Riemannian manifolds , 2001 .
[40] Yann Brenier,et al. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , 2000, Numerische Mathematik.
[41] Feng-Yu Wang,et al. Logarithmic Sobolev inequalities on noncompact Riemannian manifolds , 1997 .
[42] Patrick Cattiaux,et al. On quadratic transportation cost inequalities , 2006 .
[43] L. Gross. LOGARITHMIC SOBOLEV INEQUALITIES. , 1975 .
[44] Kaising Tso,et al. Deforming a hypersurface by its Gauss-Kronecker curvature , 1985 .
[46] R. Dobrushin. Prescribing a System of Random Variables by Conditional Distributions , 1970 .
[47] Giuseppe Savaré,et al. A new class of transport distances between measures , 2008, 0803.1235.
[48] V. Bogachev,et al. Integrability of Absolutely Continuous Transformations of Measures and Applications to Optimal Mass Transportation , 2006 .
[49] F. Cavalletti,et al. The Monge problem in Wiener space , 2011, 1103.2798.
[50] On duality theory for non-topological variants of the mass transfer problem , 1997 .
[51] B. Nazaret. Best constant in Sobolev trace inequalities on the half-space , 2006 .
[52] L. Rüschendorf. On c-optimal random variables , 1996 .
[53] Jinghai Shao,et al. Wasserstein space over the Wiener space , 2010 .
[54] R. McCann,et al. Ricci flow, entropy and optimal transportation , 2010 .
[55] N. Krylov. Fully nonlinear second order elliptic equations : recent development , 1997 .
[56] Walter Schachermayer,et al. Optimal and better transport plans , 2008, 0802.0646.
[57] Modified log-Sobolev inequalities and isoperimetry , 2006, math/0608681.
[58] К. В. Медведев,et al. Треугольные преобразования мер@@@Triangular transformations of measures , 2005 .
[59] L. Ambrosio,et al. Geodesics in the Space of Measure-Preserving Maps and Plans , 2007, math/0701848.
[60] Anatoly M. Vershik,et al. Kantorovich Metric: Initial History and Little-Known Applications , 2005 .
[61] M. Ledoux,et al. Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator , 1996 .
[62] Соболевская регулярность транспортировки вероятностных мер и транспортные неравенства , 2012 .
[63] Uniqueness and non uniqueness of optimal maps in mass transport problem with not strictly convex cost , 2010 .
[64] Mass transport generated by a flow of Gauss maps , 2008, 0803.1436.
[65] Young measures, superposition and transport , 2007, math/0701451.
[66] V. Levin. Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem , 1999 .
[67] Владимир Игоревич Богачев,et al. Интегрируемость абсолютно непрерывных преобразований мер и применения к оптимальному переносу@@@Integrability of absolutely continuous measure transformations and applications to optimal transportation , 2005 .
[68] Двойственность Монжа-Канторовича и ее применение в теории полезности , 2011 .
[69] A. Pratelli,et al. On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation , 2007 .
[70] L. Evans. Partial Differential Equations and Monge-Kantorovich Mass Transfer , 1997 .
[71] A. Guillin,et al. Transportation cost-information inequalities and applications to random dynamical systems and diffusions , 2004, math/0410172.
[72] Anatolii Moiseevich Vershik,et al. The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers , 1998 .
[73] A. Figalli,et al. A mass transportation approach to quantitative isoperimetric inequalities , 2010 .
[74] N. Trudinger,et al. On the Monge mass transfer problem , 2001 .
[75] D. A. Edwards. On the Kantorovich–Rubinstein theorem , 2011 .
[76] A proof of Sudakov theorem with strictly convex norms , 2011 .
[77] A. Üstünel,et al. Monge-Kantorovitch Measure Transportation and Monge-Ampère Equation on Wiener Space , 2004 .
[78] S. Rachev. The Monge–Kantorovich Mass Transference Problem and Its Stochastic Applications , 1985 .
[79] Xu Wang. Some counterexamples to the regularity of Monge-Ampère equations , 1995 .
[80] Соболевская регулярность для бесконечномерного уравнения Монжа-Ампера , 2012 .
[81] Guillaume Carlier,et al. From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport , 2008, SIAM J. Math. Anal..
[82] N. Gozlan. A characterization of dimension free concentration in terms of transportation inequalities , 2008, 0804.3089.
[83] C. Villani,et al. Regularity of optimal transport in curved geometry: The nonfocal case , 2010 .
[84] Sobolev regularity for the Monge-Ampere equation in the Wiener space. , 2011, 1110.1822.
[85] C. Villani,et al. Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities , 2005 .
[86] Giuseppe Savaré,et al. The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation , 2009 .
[87] V. Zolotarev. On the Continuity of Stochastic Sequences Generated by Recurrent Processes , 1976 .
[88] Paul-Marie Samson,et al. A new characterization of Talagrand's transport-entropy inequalities and applications , 2011, 1104.1303.
[89] A. Vershik. Dynamics of metrics in measure spaces and their asymptotic invariants , 2009 .
[90] V. Bogachev,et al. Nonlinear Transformations of Convex Measures , 2006 .
[91] Luigi Ambrosio,et al. Existence of optimal transport maps for crystalline norms , 2004 .
[92] X. Cabré. Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions , 2007 .
[93] Precise solutions of the one-dimensional Monge-Kantorovich problem , 2004 .
[94] O. Rothaus. Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities , 1985 .
[95] L. Rüschendorf,et al. On the Monge-Kantorovitch Duality Theorem , 2001 .
[96] S. Bobkov,et al. Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities , 1999 .
[97] Jean-Pierre Bourguignon,et al. Ricci curvature and measures , 2009 .
[98] J. Lott. Optimal transport and Perelman’s reduced volume , 2008, 0804.0343.
[99] S. Sodin,et al. An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies , 2007, math/0703857.
[100] A. Guillin,et al. Modified logarithmic Sobolev inequalities and transportation inequalities , 2004, math/0405520.
[101] C. Borell. The Brunn-Minkowski inequality in Gauss space , 1975 .
[102] Christian L'eonard,et al. Transport Inequalities. A Survey , 2010, 1003.3852.
[103] P. Cattiaux,et al. A note on Talagrand’s transportation inequality and logarithmic Sobolev inequality , 2008, 0810.5435.
[104] M. Talagrand. Transportation cost for Gaussian and other product measures , 1996 .
[105] Ludovic Rifford,et al. Mass Transportation on Sub-Riemannian Manifolds , 2008, 0803.2917.
[106] A. V. Kolesnikov. Глобальные гeльдеровы оценки для оптимальной транспортировки@@@Global Hölder Estimates for Optimal Transportation , 2008, 0810.5043.
[108] Dario Cordero-Erausquin,et al. Some Applications of Mass Transport to Gaussian-Type Inequalities , 2002 .
[109] W. Gangbo,et al. Optimal maps for the multidimensional Monge-Kantorovich problem , 1998 .
[110] Wasserstein Distance on Configuration Space , 2006, math/0602134.
[111] V. Zolotarev. METRIC DISTANCES IN SPACES OF RANDOM VARIABLES AND THEIR DISTRIBUTIONS , 1976 .
[112] G. Perelman. The entropy formula for the Ricci flow and its geometric applications , 2002, math/0211159.
[113] V. Levin. A FORMULA FOR THE OPTIMAL VALUE IN THE MONGE-KANTOROVICH PROBLEM WITH A SMOOTH COST FUNCTION, AND A CHARACTERIZATION OF CYCLICALLY MONOTONE MAPPINGS , 1992 .
[114] N. Gozlan. Characterization of Talagrand's like transportation-cost inequalities on the real line , 2006, math/0608241.
[115] W. Gangbo,et al. The geometry of optimal transportation , 1996 .
[116] Leonid Vital'evich Kantorovich (on the 100th anniversary of his birth) , 2012 .
[117] R. McCann,et al. A Riemannian interpolation inequality à la Borell, Brascamp and Lieb , 2001 .
[118] A. Figalli,et al. $W^{2,1}$ regularity for solutions of the Monge-Amp\`ere equation , 2011, 1111.7207.
[119] Emanuel Milman,et al. Properties of isoperimetric, functional and Transport-Entropy inequalities via concentration , 2009, 0909.0207.
[120] Balls have the worst best Sobolev inequalities , 2005 .
[121] A. Figalli,et al. Partial regularity of brenier solutions of the monge-ampère equation , 2010 .
[122] H. Kellerer. Duality theorems for marginal problems , 1984 .
[123] Integral Estimates for Transport Densities , 2004 .
[124] V. Oliker. Embedding Sn into Rn+1 with given integral Gauss curvature and optimal mass transport on Sn , 2007 .
[125] Young-Heon Kim,et al. A generalization of Caffarelli’s contraction theorem via (reverse) heat flow , 2010, 1002.0373.
[126] Properties of the solutions to the Monge–Ampère equation , 2004 .
[128] David A. Edwards,et al. A simple proof in Monge{Kantorovich duality theory , 2010 .
[129] A. Vershik. Many-valued measure-preserving mappings (polymorphisms) and Markovian operators , 1983 .
[130] Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities , 2009, 0902.2101.
[131] R. McCann. Existence and uniqueness of monotone measure-preserving maps , 1995 .
[132] A. Kolesnikov. Weak regularity of Gauss mass transport , 2009, 0904.1852.
[133] Karl-Theodor Sturm,et al. On the geometry of metric measure spaces , 2006 .
[134] N. Gozlan,et al. A large deviation approach to some transportation cost inequalities , 2005, math/0510601.
[135] Anatoly M. Vershik,et al. Random Metric Spaces and Universality , 2004, math/0402263.
[136] V L Levin,et al. THE PROBLEM OF MASS TRANSFER WITH A DISCONTINUOUS COST FUNCTION AND A MASS STATEMENT OF THE DUALITY PROBLEM FOR CONVEX EXTREMAL PROBLEMS , 1979 .
[137] Экстремальные свойства полупространств для сферически инвариантных мер , 1974 .
[138] A. Vershik,et al. Random Metric Spaces and Universality , 2004 .
[139] Kathrin Bacher. On Borell-Brascamp-Lieb Inequalities on Metric Measure Spaces , 2010 .
[140] G. Huisken. Flow by mean curvature of convex surfaces into spheres , 1984 .
[141] Poincare Inequalities and Moment Maps , 2011, 1104.2791.
[142] C. Villani,et al. A MASS-TRANSPORTATION APPROACH TO SHARP SOBOLEV AND GAGLIARDO-NIRENBERG INEQUALITIES , 2004 .
[143] Nicola Gigli,et al. A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions , 2010 .
[144] Нелинейные преобразования выпуклых мер@@@Nonlinear transformations of convex measures , 2005 .
[145] J. Lott. Some Geometric Calculations on Wasserstein Space , 2006, math/0612562.
[146] ON THE MONGE–AMPÈRE EQUATION IN INFINITE DIMENSIONS , 2005 .
[147] L. Rüschendorf,et al. Duality and perfect probability spaces , 1996 .
[148] M. Knott,et al. On the optimal mapping of distributions , 1984 .
[149] Global Hölder estimates for optimal transportation , 2010 .
[150] A. Kolesnikov. Convexity inequalities and optimal transport of infinite-dimensional measures , 2004 .
[151] R. Fortet,et al. Convergence de la répartition empirique vers la répartition théorique , 1953 .
[152] L. Ambrosio,et al. Existence and stability results in the L 1 theory of optimal transportation , 2003 .
[153] G. Loeper. On the regularity of solutions of optimal transportation problems , 2009 .
[154] Luis A. Caffarelli,et al. Monotonicity Properties of Optimal Transportation¶and the FKG and Related Inequalities , 2000 .
[155] N. Trudinger,et al. Interior C 2,α Regularity for Potential Functions in Optimal Transportation , 2009 .
[156] Arnaud Guillin,et al. Transportation-information inequalities for Markov processes , 2007, 0706.4193.
[157] ℒ-optimal transportation for Ricci flow , 2009 .
[158] Kazumasa Kuwada,et al. Duality on gradient estimates and Wasserstein controls , 2009, 0910.1741.
[159] Thierry Champion,et al. The Monge problem for strictly convex norms in Rd , 2010 .
[160] F. Barthe,et al. Mass Transport and Variants of the Logarithmic Sobolev Inequality , 2007, 0709.3890.
[161] S. Bobkov,et al. Hypercontractivity of Hamilton-Jacobi equations , 2001 .
[162] R. McCann,et al. Continuity, curvature, and the general covariance of optimal transportation , 2007, 0712.3077.
[163] Y. Ollivier. A survey of Ricci curvature for metric spaces and Markov chains , 2010 .
[164] C. Villani,et al. Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality , 2000 .
[165] Giuseppe Savaré,et al. Contraction of general transportation costs along solutions to Fokker–Planck equations with monotone drifts , 2010, 1002.0088.
[166] F. Otto. THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION , 2001 .
[167] Optimality Conditions and Exact Solutions to the Two-Dimensional Monge-Kantorovich Problem , 2006 .
[168] R. McCann,et al. Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport , 2006 .
[169] A. Vershik,et al. Linearly rigid metric spaces and the embedding problem , 2006, math/0611049.