On the maximal product of distances between points on a sphere
type: Item
instance of: scholarly article
title: On the maximal product of distances between points on a sphere
zbMATH Open document ID: 0890.11023
DOI: 10.1007/BF02986850
published in: Lithuanian Mathematical Journal
publication date: 1997-10-30T00:00:00Z
review text: For a set \(\{x_1, \dots, x_n\}\) of \(n\) points on the unit sphere \(S^2= \{x\in \mathbb{R}^n \mid|x|=1\}\), let \(M_n\) be the maximum of the product of their mutual euclidean distances. The determination of \(M_n\) has various mathematical and nonmathematical applications, and \(\lim M_n^{2/n(n-1)}\) for \(n\to\infty\) is called the transfinite diameter of \(S^2\). The author gives an upper bound for \(M_n\) and a lower bound for the distance of two points of the extremal (and not necessarily unique) spherical distribution.
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 11H46
Mathematics Subject Classification ID: 11H50
zbMATH DE Number: 1059785
zbMATH Keywords: maximal product of distances
zbMATH Keywords: products of linear forms
zbMATH Keywords: packings on the sphere
zbMATH Keywords: distributions on the sphere
zbMATH Keywords: points on the unit sphere
author: A. Dubickas
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Lagerung von Punkten auf der Kugel
cites work: Q3994900
cites work: Minimal discrete energy on the sphere
cites work: Punkte auf der Kugel. Drei Zusätze
cites work: Q3487498
full work available at URL: https://doi.org/10.1007/bf02986850
OpenAlex ID: W2032691160
description: scientific article; zbMATH DE number 1059785