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Optimal transport on the sub-Lorentzian Heisenberg group

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arxiv 2504.03062 v1 pith:WBIL7KP2 submitted 2025-04-03 math.MG math.DG

Samuël Borza , Wilhelm Klingenberg , Patrick Wood This is my paper · ORCID
classification math.MGmath.DG
keywords sub-lorentzianoptimaltransportgroupheisenbergbrenierderiveequation
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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.

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