Isometry Group of Gromov--Hausdorff Space

2018/06/06 by Alexander Ivanov, Ivanov, Alexander, Alexey Avgustinovich Tuzhilin +1 · 1 citation
Mathematics · #51F99 #53C23 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1806.02100

openalex publication_date 2018/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is devoted to investigation of the isometry group of the Gromov-Hausdorff space, i.e., the metric space of compact metric spaces considered up to an isometry and endowed with the Gromov-Hausdorff metric. The main goal is to present a proof of the following theorem by George Lowther (2015): The isometry group of the Gromov-Hausdorff space is trivial. Unfortunately, the author himself has not publish an accurate text for 2 years passed from the publication of draft (that is full of excellent ideas mixed with unproved and wrong statements) in the https://mathoverflow.net/ blog (see the exact reference in he bibliography).

Citations

• Realizations of Gromov-Hausdorff Distance
• Local Structure of Gromov-Hausdorff Space, and Isometric Embeddings of\n Finite Metric Spaces into this Space

Cited by

• A sequence of compact metric spaces and an isometric embedding into the Gromov-Hausdorff space

Related

• Formalizing the Gromov-Hausdorff space
• A natural compactification of the Gromov-Hausdorff space
• Isometric Embeddings of Bounded Metric Spaces into the Gromov-Hausdorff Class
• Local Structure of Gromov-Hausdorff Space, and Isometric Embeddings of\n Finite Metric Spaces into this Space
• Local Structure of Gromov-Hausdorff Space near Finite Metric Spaces in General Position