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Basic metric geometry of the bottleneck distance (2024)
Journal Article
Che, M., Galaz-García, F., Guijarro, L., Membrillo Solis, I., & Valiunas, M. (2024). Basic metric geometry of the bottleneck distance. Proceedings of the American Mathematical Society, 152(8), 3575-3591. https://doi.org/10.1090/proc/16776

Given a metric pair (X, A), i.e. a metric space X and a distinguished closed set A ⊂ X, one may construct in a functorial way a pointed pseudometric space D∞(X, A) of persistence diagrams equipped with the bottleneck distance. We investigate the basi... Read More about Basic metric geometry of the bottleneck distance.

Gromov–Hausdorff convergence of metric pairs and metric tuples (2024)
Journal Article
Ahumada Gómez, A., & Che, M. (2024). Gromov–Hausdorff convergence of metric pairs and metric tuples. Differential Geometry and its Applications, 94, Article 102135. https://doi.org/10.1016/j.difgeo.2024.102135


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, completeness and compactness theorems in this setting.... Read More about Gromov–Hausdorff convergence of metric pairs and metric tuples.

Ball covering property and number of ends of $${\mathsf {CD}}$$ spaces with non-negative curvature outside a compact set (2022)
Journal Article
Che, M., & Núñez-Zimbrón, J. (2022). Ball covering property and number of ends of $${\mathsf {CD}}$$ spaces with non-negative curvature outside a compact set. Archiv der Mathematik, 119(2), 213-224. https://doi.org/10.1007/s00013-022-01753-x

In this paper, we adapt work of Z.-D. Liu to prove a ball covering property for non-branching CD spaces with non-negative curvature outside a compact set. As a consequence, we obtain uniform bounds on the number of ends of such spaces.