18 citations · 133 across the 33 of their papers we have counts for
31 papers · 1 filter
Gromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces
Henry Adams, Semeon A. Bogatyi, Florian Frick +5
For a finite-dimensional normed space and a subset with finite Hausdorff distance from , we prove that the Gromov--Hausdorff distance between and is at least the…
Minimal Fillings of Finite Metric Spaces and Convex Polyhedra
A. O. Ivanov, A. A. Tuzhilin
Problem of minimal parametric generalized fillings of finite metric space (a version of optimal connection problem) leads to construction of a convex multidimensional polyhedra…
Fundamentals of Theory of Continuous Gromov--Hausdorff distance
Semeon A. Bogaty, Alexey A. Tuzhilin
The Gromov--Hausdorff distance (hereinafter referred to as the GH-distance) is a measure of non-isometricity of metric spaces. In this paper, we study a modification of this distan…
Calculating Gromov-Hausdorff Distance by means of Borsuk Number
Alexander O. Ivanov, Alexey A. Tuzhilin
The purpose of this article is to demonstrate the connection between the properties of the Gromov--Hausdorff distance and the Borsuk conjecture. The Borsuk number of a given bounde…
Isometric Embeddings of Bounded Metric Spaces into the Gromov-Hausdorff Class
Alexander O. Ivanov, Alexey A. Tuzhilin
It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of th…
Path Connectivity of Spheres in the Gromov-Hausdorff Class
A. Ivanov, R. Tsvetnikov, A. Tuzhilin
The paper is devoted to geometrical investigation of the Gromov-Hausdorff distance on the classes of all metric spaces and of all bounded metric spaces. The main attention is paid…