The Fermat-Torricelli problem in normed spaces

2023/04/02 by Daniil A. Ilyukhin, Ilyukhin, Daniil A.
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Aerospace Engineering and Control Systems #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2304.00550

openalex publication_date 2023/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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