THE FERMAT-TORRICELLI PROBLEM IN NORMED SPACES

被引：0

作者：

Ilyukhin, Daniil A. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Dept Differential Geometry & Applicat, Moscow, Russia

来源：

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS | 2024年 / 39卷 / 05期

关键词：

Fermat-Torricelli problem; norming functional; normed space; regular polyhedra;

D O I：

10.22190/FUMI240926065I

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：943 / 958

页数：16

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