On the distribution of weighted extremal points on a surface in \(\mathbb R^d\), \(d \geqslant 3\)
type: Item
instance of: scholarly article
title: On the distribution of weighted extremal points on a surface in \(\mathbb R^d\), \(d \geqslant 3\)
zbMATH Open document ID: 0968.31006
DOI: 10.1023/A:1026409800621
published in: Potential Analysis
publication date: 2001-02-18T00:00:00Z
review text: \textit{J. Korevaar} [Bolyai Soc. Math. Stud. 5, 35-62 (1996; Zbl 0870.31007)] raised the following problem: Given a conductor in \(\mathbb{R}^3\) with smooth boundary \(S\) and \(n\) electrons on the conductor with the ability to move freely on \(S,\) how well does the measure \(\mu_{F_n}\) associating the charge \(1/n\) with each electron, approximate the equilibrium distribution \(\mu_S\) on \(S\)? He conjectured that for ``well-behaved sets'' \(A \subset S,\) \[ |\mu_{F_n} (A)-\mu_{F}(A)|< O(1/\sqrt{n}). \] The author proves results on this and related problems. In particular, with a slightly weaker upper estimate, this type of an upper bound is proved.
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 78A30
zbMATH DE Number: 1565482
zbMATH Keywords: potential theory
zbMATH Keywords: electrons
zbMATH Keywords: conductor
zbMATH Keywords: equilibrium distribution
zbMATH Keywords: well-behaved sets
zbMATH Keywords: upper estimate
author: M. Götz
reviewed by: M. Vuorinen
MaRDI profile type: Publication
full work available at URL: a:1026409800621
OpenAlex ID: W2912359158
description: scientific article; zbMATH DE number 1565482