17 citations · 83 across the 29 of their papers we have counts for
33 papers
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…
Embeddings to Rectilinear Space and Gromov-Hausdorff Distances
A. O. Ivanov, A. A. Tuzhilin
We show that the problem whether a given finite metric space can be embedded into -dimensional rectilinear space can be reformulated in terms of the Gromov--Hausdorff distance b…
Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes
A. O. Ivanov, E. S. Lychagina, A. A. Tuzhilin
In the present paper a distinguishability of bounded metric spaces by the set of the Gromov--Hausdorff distances to so-called simplexes (metric spaces with unique non-zero distance…
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…
Gromov-Hausdorff Distance and Borsuk Number
Alexander Ivanov, Alexey Tuzhilin
The aim of this paper is to demonstrate relations between Gromov-Hausdorff distance properties and the Borsuk Conjecture. The Borsuk number of a given bounded metric space is t…