On Falconer's distance set conjecture
type: Item
instance of: scholarly article
title: On Falconer's distance set conjecture
zbMATH Open document ID: 1141.42007
DOI: 10.4171/RMI/468
published in: Revista Matemática Iberoamericana
publication date: 2007-05-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1161871350
full work available at URL: https://eudml.org/doc/41986
review text: Let \(E\) be a compact subset of \(\mathbb{R}^d\) and \(\Delta(E)=\{|x-y| : x,y \in E\}\). Falconer's conjecture is that if the Hausdorff dimension of \(E\) is greater than \(d/2\), then the Lebesgue measure of \(\Delta(E)\) is positive. In this paper the author proves that this is true if \(d > 2\) and \(\dim(E) > d(d+2)/2(d+1)\).
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 5152585
zbMATH Keywords: Fourier restriction estimates
zbMATH Keywords: Frostman measures
zbMATH Keywords: Falconer's conjecture
author: Mehmet Burak Erdoğan
reviewed by: Delfina Roux
MaRDI profile type: Publication
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Wikidata QID: Q123236156
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description: scientific article; zbMATH DE number 5152585