25 citations · 56 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
Optimal transport between algebraic hypersurfaces
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing t…
A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
The scope of this survey is to give a self-contained introduction to synthetic timelike Ricci curvature bounds for (possibly non-smooth) Lorentzian spaces via optimal transport $\&…
Quantitative isoperimetry à la Levy-Gromov
F. Cavalletti, F. Maggi, A. Mondino
On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap be…