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math.DG2026
Ollivier-Ricci curvature for causal sets
Joe Barton, Samuël Borza, Jona Röhrig
We introduce a novel notion of Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport. The construction is motivated by a new Lorentzian asymptotic formula of…
math.DG2026
A Splitting Theorem for non-positively curved Lorentzian spaces
Joe Barton, Tobias Beran, Mauricio Che +3
We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any ti…