From the 1 of 4 linked papers with an AI index.
4 papers
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
The paper introduces a notion of submetries adapted to Lorentzian spacetimes, proves that under completeness they coincide with locally C^{1,1} semi‑Riemannian submersions, and app…
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…