We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.
|Original language||English (US)|
|Number of pages||32|
|Journal||Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques|
|State||Published - Jun 27 2015|
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