English

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.

Keywords

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}
}

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34 pages