Duality and existence for a class of mass transportation problems and economic applications

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Free boundaries in optimal transport and Monge-Ampere obstacle problems (2010, background): “Injectivity of y ! r xc(x0,y) is a familiar criterion from Gangbo [38], Carlier [ 21 ], and Ma, Trudinger & Wang for uniqueness of total transfer; it follows from strict convexity in Caarelli [18] and Gangbo & McCann [39].”
Matching for teams (2010, result): “We refer to [1] for a proof of this result.”
Rearrangement inequalities in non-convex insurance models (2005, unknown): “For similar results in a multidimensional type framework and more general measures we refer to [5].”
Pareto efficient insurance contracts when the insurer's cost function is discontinuous (2003, background): “The proof of 1) is rather standard and a proof can be found in [ 5 ].”
Continuity, curvature, and the general covariance of optimal transportation (2007, result): “Although Monge’s problem is more subtle to solve than Kantorovich’s, when M is a smooth manifold and ρ vanishes on every Lipschitz submanifold of lower dimension, a twist condition ((A1), Definition 2.1 below) on the cost function c(x, x̄) guarantees existence and uniqueness of an optimal map F , as”
Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness (2007, methodology): “Carlier and Ekeland (2009) study this problem and establish existence of equilibrium.”