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gr-qc2026
The Null Energy Condition through the Lens of Optimal Transport: Smooth and Non-Smooth Spacetimes
Fabio Cavalletti, Davide Manini, Andrea Mondino
We survey recent developments on the null energy condition (NEC) from the perspective of optimal transport, with emphasis on non-smooth Lorentzian geometry. After recalling the rol…
math.DG2026
A singularity theorem in terms of asymptotic expansion
Fabio Cavalletti, Andrea Mondino
We prove a sharp singularity theorem in which the classical focusing hypothesis of Hawking--Penrose theory is replaced by a condition on the asymptotic volume growth of timelike ge…