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In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y).
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H. Tanaka · 1973
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A necessary and sufficient condition for rationalizability in a quasi-linear context
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On the optimal transportation of distributions
C. Smith and M. Knott · 1987
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Multidimensional incentive compatibility and mechanism design
R.P. McAfee and J. McMillan · 1988
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Notes on the Wasserstein metric in Hilbert spaces
J.A. Cuesta-Albertos and C. Matrán · 1989
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Properties of the Lagrangian semi-geostrophic equations
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Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
P. Delanoë · 1991
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Bounds for distributions with multivariate marginals
L. Rüschendorf · 1991
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Boundary regularity of maps with convex potentials
L.A. Caffarelli · 1992
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The regularity of mappings with a convex potential
L.A. Caffarelli · 1992
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On Hoeffding-Fréchet bounds and cyclic monotone relations
C. Smith and M. Knott · 1992
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A characterization for the solution of the Monge-Kantorovich mass transference problem
J.A. Cuesta-Albertos and A. Tuero-Díaz · 1993
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Sur la distance de deux lois dans le cas vectoriel
T. Abdellaoui and H. Heinich · 1994
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A Convexity Theory for Interacting Gases and Equilibrium Crystals
R.J. McCann · 1994
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Isoperimetric inequalities for quermassintegrals
N.S. Trudinger · 1994
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Habilitation thesis
W. Gangbo · 1995
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Optimal maps in Monge’s mass transport problem
W. Gangbo and R.J. McCann · 1995
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Existence and uniqueness of monotone measure-preserving maps
R.J. McCann · 1995
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Optimal solutions of multivariate coupling problems
L. Rüschendorf · 1995
Cited alongside, same era.
Multiproduct nonlinear pricing
M. Armstrong · 1996
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Allocation maps with general cost functions
L. Caffarelli · 1996
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Boundary regularity of maps with convex potentials — II
L.A. Caffarelli · 1996
Newton’s problem of the body of minimal averaged resistance (Russian)
A.Yu. Plakhov · 2004
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On the design of a reflector antenna II
X.-J. Wang · 2004
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Gradient flows in metric spaces and in the space of probability measures
L.A. Ambrosio, N. Gigli, and G. Savaré · 2005
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Multidimensional Screening
S. Basov · 2005
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An optimal matching problem
I. Ekeland · 2005
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Regularity of potential functions of the optimal transportation problem
X.-N. Ma, N. Trudinger and X.-J. Wang · 2005
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The geometry of optimal transportation
W. Gangbo and R.J. McCann · 1996
Cited alongside, same era.
On c c -optimal random variables
L. Rüschendorf · 1996
Cited alongside, same era.
On the design of a reflector antenna
X.-J. Wang · 1996
Cited alongside, same era.
A convexity principle for interacting gases
R.J. McCann · 1997
Cited alongside, same era.
On the second boundary value problem for equations of Monge-Ampère type
J. Urbas · 1997
Cited alongside, same era.
M.-K. von Renesse and K.-T. Sturm · 2005
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Contractions in the 2 2 -wasserstein length space and thermalization of granular media
J.A. Carrillo, R.J. McCann, and C. Villani · 2006
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Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
D. Cordero-Erausquin, R.J. McCann and M. Schmuckenschläger · 2006
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A Mathematical Theory of Large Scale Atmosphere/Ocean Flows
M.J.P. Cullen · 2006
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Stable rotating binary stars and fluid in a tube
R.J. McCann · 2006
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On the geometry of metric measure spaces, I and II
K.-T. Sturm · 2006
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Conformal geometry and fully nonlinear equations
J.A. Viaclovsky · 2006
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Optimal mass transportation and Mather theory
P. Bernard and B. Buffoni · 2007
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The formation of a tree leaf
Q. Xia · 2007
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Michell trusses and lines of principal action
G. Bouchitté, W. Gangbo and P. Seppecher · 2008
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Equilibrium structure of a bidimensional asymmetric city
G. Carlier and I. Ekeland · 2008
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The ∞ \infty -Wasserstein distance: local solutions and existence of optimal transport maps
T. Champion, L. De Pascale, and P. Juutinen · 2008
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Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds
Y.-H. Kim · 2008
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Balls have the worst best Sobolev inequalities. II. Variants and extensions
F. Maggi and C. Villani · 2008
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Optimal Transportation Networks: Models and Theories
M. Bernot, V. Caselles, J.-M. Morel · 2009
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C 1 C^{1} regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two
A. Figalli and G. Loeper · 2009
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Continuity of optimal transport maps on small deformations of 𝕊 2 \mathbb{S}^{2}
A. Figalli and L. Rifford · 2009
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Smooth optimal transportation on hyperbolic space
J. Li · 2009
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Hölder regularity of optimal mappings in optimal transportation
J. Liu · 2009
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On the regularity of solutions of optimal transportation problems
G. Loeper · 2009
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Optimal transport and Perelman’s reduced volume
J. Lott · 2009
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Ricci curvature for metric measure spaces via optimal transport
J. Lott and C. Villani · 2009
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ℒ {\mathcal{L}} -optimal transportation for Ricci flow
P. Topping · 2009
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On the second boundary value problem for Monge-Ampère type equations and optimal transportation
N.S. Trudinger and X.-J. Wang · 2009
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Optimal Transport. Old and New
C. Villani · 2009
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Free boundaries in optimal transport and Monge-Ampère obstacle problems
L.A. Caffarelli and R.J. McCann · 2010
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Hedonic price equilibria, stable matching and optimal transport: equivalence, topology and uniqueness
P.-A. Chiappori, R.J. McCann, and L. Nesheim · 2010
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Optimal transportation on non-compact manifolds
A. Fathi and A. Figalli · 2010
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Continuity, curvature, and the general covariance of optimal transportation
Y.-H. Kim and R.J. McCann · 2010
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Interior C 2 , α C^{2,\alpha} regularity for potential functions in optimal transportation
J. Liu, N.S. Trudinger, X.-J. Wang · 2010
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Regularity of optimal transport in curved geometry: the non-focal case
G. Loeper and C. Villani · 2010
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Ricci flow, entropy, and optimal transportation
R.J. McCann and P. Topping · 2010
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Personal communication
B. Pass · 2010
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