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math.DG2026
Total curvature and length estimates for timelike curves in Lorentzian length spaces
Darius Erös, Felix Rott, Zhe-Feng Xu
We introduce and study a synthetic notion of timelike total curvature for curves in Lorentzian length spaces with upper curvature bounds. In particular, we prove that our notion ag…
math.DG2026
Lorentz meets Ptolemy
Felix Rott, Zhe-Feng Xu, Matteo Zanardini
We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curva…