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On the local structure of optimal measures in the multi-marginal optimal transportation problem

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Abstract

We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension of the support of the solution.

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  1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E3, Canada

    Brendan Pass

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  1. Brendan Pass
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Correspondence to Brendan Pass.

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Communicated by L. Ambrosio.

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Pass, B. On the local structure of optimal measures in the multi-marginal optimal transportation problem. Calc. Var. 43, 529–536 (2012). https://doi.org/10.1007/s00526-011-0421-z

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  • DOI: https://doi.org/10.1007/s00526-011-0421-z

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