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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.MG2023
The Fermat-Torricelli problem in normed spaces
Daniil A. Ilyukhin
The article studies a generalization of the classical Fermat-Torricelli problem to normed spaces of arbitrary finite dimension. Necessary and sufficient conditions for the uniquene…
math.MG2022
The Fermat-Torricelli problem in the case of three-point sets in normed planes
D. A. Ilyukhin
In the paper the Fermat-Torricelli problem is considered. The problem asks a point minimizing the sum of distances to arbitrarily given points in d-dimensional real normed spaces.…