15 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…
Positive resolution of Bartnik's cosmological splitting conjecture
Robert J. McCann, Argam Ohanyan
We give a proof of the cosmological splitting conjecture of Robert Bartnik from 1988, which expresses the rigidity of the cosmological Hawking--Penrose singularity theorem. It stat…
Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations
Gregory J. Galloway, Robert J. McCann, Argam Ohanyan
The families of Lorentzian distance functions to and from points along a complete timelike line in a spacetime are known to be locally equi-Lipschitz continuous in a neighborhood o…
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…
Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs
Argam Ohanyan, Marta Sálamo Candal
We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form , where is a suitable m…
Splitting theorems for weighted Finsler spacetimes via the -d'Alembertian: beyond the Berwald case
Erasmo Caponio, Argam Ohanyan, Shin-ichi Ohta
A timelike splitting theorem for Finsler spacetimes was previously established by the third author, in collaboration with Lu and Minguzzi, under relatively strong hypotheses, inclu…