Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications

Journal article

The goal of the present work is three-fold. The first goal is to set foundational results on optimal transport in Lorentzian (pre-)length spaces, including cyclical monotonicity, stability of optimal couplings and Kantorovich duality (several results are new even for smooth Lorentzian manifolds). The second one is to give a synthetic notion of “timelike Ricci curvature bounded below and dimension bounded above” for a measured Lorentzian pre-length space using optimal transport. The key idea b...

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Authors: Cavalletti, F; Mondino, A

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: International Press of Boston
• Journal: Cambridge Journal of Mathematics
• Acceptance date: 2023-09-25
• EISSN: 2168-0949
• ISSN: 2168-0930
• Language: English
• Keywords: math-ph; FFR; math.MP; math.MG; math.DG; math.OC