3 papers
math.MG2026
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…
math.MG2026
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…
math.MG2025
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…