6 papers
Almost-splitting of spacetimes under timelike sectional curvature bounds
Nicola Gigli, Melanie Graf, Robert J. McCann +3
We establish an almost-splitting theorem for spacetimes under timelike sectional curvature bounds in the spirit of the celebrated Riemannian result due to Cheeger and Colding. More…
Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime
Nicola Gigli, Argam Ohanyan, Marco Picerni +2
We study the directed completion of Lorentzian pre-length spaces, and we show that, under some natural assumptions which cover the case of smooth globally hyperbolic spacetimes, it…
Submetries in non-positive signature and applications
Matteo Zanardini
We consider a generalization of the notion of submetry tailored to the setting of spacetimes. We show that, under suitable completeness assumptions, Lorentzian submetries between s…
Lorentz meets Ptolemy
Felix Rott, Zhe-Feng Xu, Matteo Zanardini
We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curva…
PDE aspects of the dynamical optimal transport in the Lorentzian setting
Nicola Gigli, Felix Rott, Matteo Zanardini
One of the crucial features of optimal transport on Riemannian manifolds is the equivalence of the `static', original, formulation of the problem and of the `dynamic' one, based on…
Microstructures and anti-phase boundaries in long-range lattice systems
Andrea Braides, Edoardo Voglino, Matteo Zanardini
We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions a…