|
The Fermat–Torricelli problem in the case of three-point sets in normed planes
D. A. Ilyukhin Lomonosov Moscow State University (Moscow)
Abstract:
In the paper the Fermat–Torricelli problem is considered. The problem asks a point minimizing the sum of distances to arbitrarily given points in $d$-dimensional real normed spaces. Various generalizations of this problem are outlined, current methods of solving and some recent results in this area are presented. The aim of the article is to find an answer to the following question: in what norms on the plane is the solution of the Fermat–Torricelli problem unique for any three points. The uniqueness criterion is formulated and proved in the work, in addition, the application of the criterion on the norms set by regular polygons, the so-called lambda planes, is shown.
Keywords:
Fermat–Torricelli problem, norming functional, lambda-plane.
Received: 15.06.2022 Accepted: 22.12.2022
Citation:
D. A. Ilyukhin, “The Fermat–Torricelli problem in the case of three-point sets in normed planes”, Chebyshevskii Sb., 23:5 (2022), 72–86
Linking options:
https://www.mathnet.ru/eng/cheb1256 https://www.mathnet.ru/eng/cheb/v23/i5/p72
|
Statistics & downloads: |
Abstract page: | 81 | Full-text PDF : | 43 | References: | 20 |
|