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arXiv · 2003.10727

Multi-marginal optimal transport on the Heisenberg group

Brendan Pass·Andrea Pinamonti·Mattia Vedovato
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Abstract

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-Carath\'eodory 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.

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Brendan Pass, Andrea Pinamonti, Mattia Vedovato. 2020-03-24. Multi-marginal optimal transport on the Heisenberg group. https://arxiv.org/abs/2003.10727

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