The Fermat-Torricelli problem in normed spaces
| Autor: | Ilyukhin, Daniil A. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 16 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2210.04374 |
| Databáze: | arXiv |
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