13 papers
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…
Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces
Andrea Mondino, Raquel Perales
We consider metric measure spaces satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these a…
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…
On the rectifiability of and spaces with unique tangents
Mattia Magnabosco, Andrea Mondino, Tommaso Rossi
We prove rectifiability results for and metric measure spaces with pointwise Ahlfors regular reference…
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…
A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds
Fabio Cavalletti, Andrea Mondino
The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The…