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A Convexity Principle for Interacting Gases
A new set of inequalities is introduced, based on a novel but natural interpolation between Borel probability measures on R d . Using these estimates in lieu of convexity or rearrangementExpand
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Polar factorization of maps on Riemannian manifolds
Abstract. Let (M,g) be a connected compact manifold, C3 smooth and without boundary, equipped with a Riemannian distance d(x,y). If $ s : M \to M $ is merely Borel and never maps positive volumeExpand
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The geometry of optimal transportation
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 1. Summary of main results . . . . . . . . . . . . . . . . . . . . . . . . 120 2. Background on optimalExpand
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Existence and uniqueness of monotone measure-preserving maps
Introduction. Given a pair of Borel probability measures # and v on Rd, it is natural to ask whether v can be obtained from # by redistributing its mass in a canonical way. In the case of the line dExpand
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Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4]Expand
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A Family of Nonlinear Fourth Order Equations of Gradient Flow Type
Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on R d are studied. These equations constitute gradient flows for the perturbedExpand
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Free boundaries in optimal transport and Monge-Ampere obstacle problems
Given compactly supported 0 f,g 2 L 1 (R n ), the problem of trans- porting a fraction m min{kfkL1,kgkL1} of the mass of f onto g as cheaply as possible is considered, where cost per unit massExpand
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Continuity, curvature, and the general covariance of optimal transportation
Let M and M be n-dimensional manifolds equipped with suitable Borel probability measures ρ and ρ. For subdomains M and M of Rn, Ma, Trudinger & Wang gave sufficient conditions on a transportationExpand
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Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particlesExpand
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When is multidimensional screening a convex program?
TLDR
A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Expand
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