7 papers
Doubling for chronological diamonds in Lorentzian geometry
Mauricio Che, Sebastian Gieger, Clemens Sämann
We define doubling conditions for measured Lorentzian length spaces in terms of chronological diamonds, and prove that such conditions are implied by suitable timelike curvature bo…
Timelike ideal boundary of non-positively curved Lorentzian spaces
Saúl Burgos, Mauricio Che, Miguel Prados-Abad
We introduce the notion of timelike ideal boundary of a Lorentzian length space as the set of asymptotic classes of future or past-directed timelike geodesic rays, a construction c…
Convergence of Timed-Metric Spaces and Causality
Mauricio Che, Raquel Perales
We introduce the notion of timed-Gromov--Hausdorff distance for timed-metric spaces. We prove that this distance is bi-Lipschitz equivalent to the intrinsic timed-Hausdorff distanc…
Gromov's Compactness Theorem for the Intrinsic Timed-Hausdorff Distance
Mauricio Che, Raquel Perales, Christina Sormani
The intrinsic timed-Hausdorff distance between timed-metric spaces, first introduced by Sakovich--Sormani, yields a weak notion of convergence for space-times. In this paper we pro…
A Splitting Theorem for non-positively curved Lorentzian spaces
Joe Barton, Tobias Beran, Mauricio Che +3
We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any ti…
Optimal partial transport for metric pairs
Mauricio Che
In this article we study Figalli and Gigli's formulation of optimal transport between non-negative Radon measures in the setting of metric pairs. We carry over classical characteri…