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arXiv:math/0412299 [math.DS]AbstractReferencesReviewsResources

Optimal mass transportation and Mather theory

Patrick Bernard, Boris Buffoni

Published 2004-12-15, updated 2007-01-16Version 2

We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are inspired from Mather theory on Lagrangian systems. We make use of viscosity solutions of the associated Hamilton-Jacobi equation in the spirit of Fathi's approach to Mather theory.

Journal: Journal of the European Mathematical Society 9 (2007) 85-121
Categories: math.DS, math.AP, math.PR
Subjects: 49Q20, 70H20, 49L20
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