Isometry Group of Gromov--Hausdorff Space

zbMath1474.53209arXiv1806.02100MaRDI QIDQ4988579

A. A. Tuzhilin, Alexandr O. Ivanov

Publication date: 17 May 2021

Full work available at URL: https://arxiv.org/abs/1806.02100

zbMATH Keywords

isometry groupsGromov-Hausdorff distancemetric geometryGromov-Hausdorff spacecompact metric spaces

Mathematics Subject Classification ID

Metric geometry (51F99) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Compact (locally compact) metric spaces (54E45)

Related Items (7)

Unnamed Item ⋮ Characterization of Gromov-type geodesics ⋮ On inductive and inverse limits of systems of compact metric spaces and applications ⋮ Path connectivity of spheres in the Gromov-Hausdorff class ⋮ Unnamed Item ⋮ Local geometry of the Gromov-Hausdorff metric space and totally asymmetric finite metric spaces ⋮ The Fermat-Steiner problem in the space of compact subsets of endowed with the Hausdorff metric

Uses Software

• MathOverflow

Cites Work

• Unnamed Item
• Some properties of Gromov-Hausdorff distances
• The Gromov-Hausdorff metric on the space of compact metric spaces is strictly intrinsic
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Local structure of Gromov-Hausdorff space, and isometric embeddings of finite metric spaces into this space
• On quasi‐isometric mappings, I

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