3 papers
math.DG2026
A singularity theorem in terms of asymptotic expansion
Fabio Cavalletti, Andrea Mondino
We prove a singularity theorem in which the classical focusing hypothesis of Hawking--Penrose theory is replaced by a condition on asymptotic volume growth. Under the strong energy…
math.DG2026
On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino
This paper develops a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent…
math.DG2025
Optimal transport on null hypersurfaces and the null energy condition
Fabio Cavalletti, Davide Manini, Andrea Mondino
The goal of the present work is to study optimal transport on null hypersurfaces inside Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface…