24 citations · 52 across the 18 of their papers we have counts for
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…
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…
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…