Calculus of Variations and Geometric Measure Theory

B. Pass - A. Pinamonti - M. Vedovato

Multi-marginal optimal transport on the Heisenberg group

created by pinamonti on 20 Mar 2020
modified on 06 Nov 2020


Accepted Paper

Inserted: 20 mar 2020
Last Updated: 6 nov 2020

Journal: Methods and Applications of Analysis
Year: 2020

ArXiv: 2003.10727 PDF

Dedicated to Professor John Urbas’ 60th birthday.


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.