On Falconer's distance set conjecture (Q879632)
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scientific article; zbMATH DE number 5152585
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Falconer's distance set conjecture |
scientific article; zbMATH DE number 5152585 |
Statements
On Falconer's distance set conjecture (English)
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14 May 2007
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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 \(\dim(E) > d(d+2)/2(d+1)\).
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Fourier restriction estimates
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Frostman measures
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Falconer's conjecture
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0.9415288
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0.9403008
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0.9165158
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0.89547086
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0.89291656
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0.88406426
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