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Optimal transport on the sub-Lorentzian Heisenberg group

Published 3 Apr 2025 in math.MG and math.DG | (2504.03062v1)

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.

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