Email this article Isometric embeddings of bounded metric spaces in the Gromov-Hausdorff class
- Authors: Ivanov A.O.1,2,3, Tuzhilin A.A.1
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Bauman Moscow State Technical University
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 213, No 10 (2022)
- Pages: 90-107
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133470
- DOI: https://doi.org/10.4213/sm9729
- ID: 133470
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Abstract
We show that any bounded metric space can be embedded isometrically in the Gromov-Hausdorff metric class $\operatorname{\mathcal{GH}}$. This is a consequence of the description of the local geometry of $\operatorname{\mathcal{GH}}$ in a sufficiently small neighbourhood of a generic metric space, which is of independent interest. We use the techniques of optimal correspondences and their distortions.Bibliography: 22 titles.
About the authors
Alexandr Olegovich Ivanov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Bauman Moscow State Technical University; Moscow Center for Fundamental and Applied Mathematics
Email: aoiva@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
Alexey Avgustinovich Tuzhilin
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: tuz@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
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