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Publications Influence

A Convexity Principle for Interacting Gases

- R. McCann
- Mathematics
- 1 June 1997

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 rearrangement… Expand

723 107- PDF

Polar factorization of maps on Riemannian manifolds

- R. McCann
- Mathematics
- 1 August 2001

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 volume… Expand

389 71- PDF

The geometry of optimal transportation

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 1. Summary of main results . . . . . . . . . . . . . . . . . . . . . . . . 120 2. Background on optimal… Expand

712 68- PDF

Existence and uniqueness of monotone measure-preserving maps

- R. McCann
- Mathematics
- 1 November 1995

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 d… Expand

363 51- PDF

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

- J. Carrillo, R. McCann, C. Villani
- Mathematics
- 31 December 2003

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

389 37- PDF

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

- D. Matthes, R. McCann, Giuseppe Savare'
- Physics, Mathematics
- 5 January 2009

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 perturbed… Expand

131 27- PDF

Free boundaries in optimal transport and Monge-Ampere obstacle problems

- L. Caffarelli, R. McCann
- Mathematics
- 7 July 2010

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 mass… Expand

109 19- PDF

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 transportation… Expand

132 19- PDF

Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media

- J. A. Carrillo, R. McCann, C. Villani
- Mathematics
- 1 February 2006

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 particles… Expand

297 18- PDF

When is multidimensional screening a convex program?

- A. Figalli, Y. Kim, R. McCann
- Mathematics, Computer Science
- J. Econ. Theory
- 15 December 2009

TLDR

86 13- PDF