THE FERMAT-TORRICELLI PROBLEM IN NORMED SPACES

Daniil A. Ilyukhin

DOI Number
https://doi.org/10.22190/FUMI240926065I
First page
943
Last page
958

Abstract


The article studies a generalization of the classical Fermat-Torricelli problem to normed spaces of arbitrary finite dimension. Given integer n, we describe all normed spaces such that the solution of the Fermat-Torricelli problem is unique for any n points in this space. More precise conditions for normed planes and three-dimensional spaces are presented. In addition, we apply the criterion to norms whose unit balls are regular polyhedra.

Keywords

Fermat-Torricelli problem, norming functional, normed space, regular polyhedra.

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References


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DOI: https://doi.org/10.22190/FUMI240926065I

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ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)