I. N. Mikhailov

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math.MG2025

Calculating Gromov-Hausdorff distance by means of asymptotic dimension

Ivan N. Mikhailov

In this paper, we apply the concept of asymptotic dimension to calculating Gromov-Hausdorff distances between some unbounded metric spaces. For example, we show that the Gromov--Ha…

math.MG2024

Gromov-Hausdorff Geometry of Metric Trees

A. O. Ivanov, I. N. Mikhailov, A. A. Tuzhilin

In this paper, we study metric trees, without any finiteness restrictions. For subsets of such trees, a condition that guarantees that the Hausdorff and Gromov--Hausdorff distances…

math.MG2024

When the Gromov-Hausdorff distance between finite-dimensional space and its subset is finite?

I. N. Mikhailov, A. A. Tuzhilin

In this paper we prove that the Gromov--Hausdorff distance between $R^{n}$ and its subset $A$ is finite if and only if $A$ is an $ε$ -net in $R^{n}$ for some…

math.MG2024

Gromov-Hausdorff distances between normed spaces

I. N. Mikhailov

In the present paper we study the original Gromov-Hausdorff distance between real normed spaces. In the first part of the paper we prove that two finite-dimensional real normed spa…