6 papers
Intrinsic Timed Hausdorff Convergence and Its Implications
Raquel Perales
Sakovich--Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov-Hausdorff distances and there…
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…
Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces
Andrea Mondino, Raquel Perales
We consider metric measure spaces satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these a…
Monotone Sequences of Metric Spaces with Compact Limits
R. Perales, C. Sormani
In this paper, we consider a fixed metric space (possibly an oriented Riemannian manifold with boundary) with an increasing sequence of distance functions and a uniform upper bound…
Volume entropy and rigidity for RCD-spaces
Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map from a non-collapsed RCD$(-(N-1),…