Inserted: 20 mar 2020
Last Updated: 25 mar 2020
We consider the multi-marginal optimal transport of aligning sev- eral compactly supported marginals on the Heisenberg group to mini- mize 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.