4 papers · 1 filter
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…
Metric pairs and tuples in theory and applications
Andrés Ahumada Gómez, Mauricio Che, Manuel Cuerno
We present theoretical properties of the space of metric pairs equipped with the Gromov--Hausdorff distance. First, we establish the classical metric separability and the geometric…
Isometric Rigidity of Metric Constructions with respect to Wasserstein Spaces
Mauricio Che, Fernando Galaz-García, Martin Kerin +1
In this paper we study the isometric rigidity of certain classes of metric spaces with respect to the -Wasserstein space. We prove that spaces that split a separable Hilbert spa…