7 citations · 15 across the 11 of their papers we have counts for
13 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…
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…
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…
FEVER-OOD: Free Energy Vulnerability Elimination for Robust Out-of-Distribution Detection
Brian K. S. Isaac-Medina, Mauricio Che, Yona F. A. Gaus +2
Modern machine learning models, that excel on computer vision tasks such as classification and object detection, are often overconfident in their predictions for Out-of-Distributio…
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…
On spaces with nonnegative curvature outside a compact set
Mauricio Che, Jesús Núñez-Zimbrón
In this paper we adapt work of Z.-D. Liu to prove a ball covering property for non-branching spaces with nonnegative curvature outside a compact set. As a consequence…