A. O. Ivanov, A. A. Tuzhilin, “Isometric embeddings of bounded metric spaces in the Gromov-Hausdorff class”, Mat. Sb., 2022, Volume 213, Number 10,Pages <nobr>90

This article is cited in 3 papers

Isometric embeddings of bounded metric spaces in the Gromov-Hausdorff class

A. O. Ivanov^abc, A. A. Tuzhilin^a

^a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Bauman Moscow State Technical University, Moscow, Russia
^c Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

Abstract: We show that any bounded metric space can be embedded isometrically in the Gromov-Hausdorff metric class $\operatorname{\mathcal{G\!H}}$. This is a consequence of the description of the local geometry of $\operatorname{\mathcal{G\!H}}$ 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.

Keywords: Gromov-Hausdorff distance, class of all metric spaces, von Neumann-Bernays-Gödel axioms, isometric embedding of a bounded metric space, generic metric space.

MSC: Primary 51F99, 51K05, 53C23; Secondary 54B20

Received: 04.02.2022

DOI: 10.4213/sm9729