25 citations · 56 across the 8 of their papers we have counts for
9 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…
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…
A proof of the Hamiltonian Thom Isotopy Lemma
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
In this note we present a complete proof of the fact that all the submanifolds of a one parameter family of compact symplectic submanifolds inside a compact symplectic manifold are…
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…
Rigidities of Isoperimetric inequality under nonnegative Ricci curvature
Fabio Cavalletti, Davide Manini
The sharp isoperimetric inequality for non-compact Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth has been obtained in increasing generality wit…
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…