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Multi-marginal optimal transport on the Heisenberg group

We consider the multi-marginal optimal transport of aligning several compactly supported marginals on the Heisenberg group to minimize the total cost, which we take to be the sum of the squared Carnot-Carathéodory distances from the marginal points to their barycenter. Under certain technical hypotheses, we prove existence and uniqueness of optimal maps. We also point out several related open questions.

preprint2020arXivOpen access
Brendan PassAndrea PinamontiMattia Vedovato
math.APmath.OC
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Brendan PassAndrea PinamontiMattia Vedovato

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