5 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…
An elliptic proof of the splitting theorems from Lorentzian geometry
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We ex…
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…
A Lorentzian splitting theorem for continuously differentiable metrics and weights
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity by combining elliptic techniques for the negative homogeneity…
A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes
Tobias Beran, Mathias Braun, Matteo Calisti +5
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the r…