The Fermat-Torricelli problem in normed spaces
Metric Geometry
2023-04-04 v1
Abstract
The article studies a generalization of the classical Fermat-Torricelli problem to normed spaces of arbitrary finite dimension. Necessary and sufficient conditions for the uniqueness of the solution of the Fermat-Torricelli problem for any n points in a fixed space are obtained, and more precise conditions for normed planes and three-dimensional spaces are presented. In addition, examples of the application of the criterion in the norms given by regular polyhedra are given.
Cite
@article{arxiv.2304.00550,
title = {The Fermat-Torricelli problem in normed spaces},
author = {Daniil A. Ilyukhin},
journal= {arXiv preprint arXiv:2304.00550},
year = {2023}
}
Comments
16 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2210.04374