Gromov–Hausdorff convergence of metric pairs and metric tuples

Ahumada Gómez, Andrés; Che, Mauricio

Abstract

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. Finally, we get a relative version of Fukaya's theorem about quotient spaces under Gromov–Hausdorff equivariant convergence and a version of Grove–Petersen–Wu's finiteness theorem for stratified spaces.

Citation

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

• Journal Article Type: Article
• Acceptance Date: Mar 17, 2024
• Online Publication Date: Apr 2, 2024
• Publication Date: 2024-06
• Deposit Date: May 9, 2024
• Publicly Available Date: May 9, 2024
• Journal: Differential Geometry and its Applications
• Print ISSN: 0926-2245
• Electronic ISSN: 1872-6984
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 94
• Article Number: 102135
• DOI: https://doi.org/10.1016/j.difgeo.2024.102135
• Public URL: https://durham-repository.worktribe.com/output/2378596