On Falconer’s distance set problem in the plane
By Larry Guth, Alex Iosevich, Yumeng Ou, Hong Wang. Inventiones Mathematicae, 2018
193 citations recorded by the source corpus.
If E⊂R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E \subset \mathbb {R}^2$$\end{document} is a compact set of Hausdorff dimension greater than 5 / 4, we prove that there is a point x∈E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x \in E$$\end{document} so that the set of distances {|x-y|}y∈E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{ |x-y| \}_{y \in E}$$\end{document} has positive Lebesgue measure.
Subfields: Geometry and Topology, Mathematical Physics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/c701c68236e34856d7d9d41675fec1ae78095df8
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In Geometry and Topology
In Mathematical Physics
In Numerical Analysis
Citations in the corpus
- Assouad Dimension and Fractal Geometry (2020, background): “That said, since 2010 the problem has been receiving a lot of attention in the literature, and significant progress is being made, see for example, [252, 253, 225, 167, 124].”