Optimal transport on the sub-Lorentzian Heisenberg group
Metric Geometry
2025-04-07 v1 Differential Geometry
Abstract
We investigate the synthetic metric spacetime structure of the sub-Lorentzian Heisenberg group and we study the optimal transport problem in this space. The sub-Lorentzian version of Brenier's theorem is established in this setting. Finally, we provide examples of optimal transport maps and derive a sub-Lorentzian Monge-Amp\`ere equation.
Cite
@article{arxiv.2504.03062,
title = {Optimal transport on the sub-Lorentzian Heisenberg group},
author = {Samuël Borza and Wilhelm Klingenberg and Patrick Wood},
journal= {arXiv preprint arXiv:2504.03062},
year = {2025}
}
Comments
34 pages