5 papers · 1 filter
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…
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…
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…
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…