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