7 citations · 15 across the 11 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
Gromov-Hausdorff convergence of metric pairs and metric tuples
Andrés Ahumada Gómez, Mauricio Che
We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, com…
Basic Metric Geometry of the Bottleneck Distance
Mauricio Che, Fernando Galaz-García, Luis Guijarro +2
Given a metric pair , i.e. a metric space and a distinguished closed set , one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\…
Metric Geometry of Spaces of Persistence Diagrams
Mauricio Che, Fernando Galaz-García, Luis Guijarro +1
Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces o…