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arXiv · 1003.4556

Rectifiability of Optimal Transportation Plans

Robert J. McCann·Brendan Pass·Micah Warren
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Abstract

The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere.

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Robert J. McCann, Brendan Pass, Micah Warren. 2010-03-23. Rectifiability of Optimal Transportation Plans. https://doi.org/10.4153/cjm-2011-080-6

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