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arXiv · 1212.1680

Remarks on multi-marginal symmetric Monge-Kantorovich problems

Nassif Ghoussoub·Bernard Maurey
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Abstract

Symmetric Monge-Kantorovich transport problems involving a cost function given by a family of vector fields were used by Ghoussoub-Moameni to establish polar decompositions of such vector fields into $m$-cyclically monotone maps composed with measure preserving $m$-involutions ($m\geq 2$). In this note, we relate these symmetric transport problems to the Brenier solutions of the Monge and Monge-Kantorovich problem, as well as to the Gangbo-\'Swi\c{e}ch solutions of their multi-marginal counterparts, both of which involving quadratic cost functions.

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Nassif Ghoussoub, Bernard Maurey. 2012-12-07. Remarks on multi-marginal symmetric Monge-Kantorovich problems. https://arxiv.org/abs/1212.1680

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