On Falconer’s distance set problem in the plane

Larry Guth; Alex Iosevich; Yumeng Ou; Hong Wang

doi:10.1007/s00222-019-00917-x

On Falconer’s distance set problem in the plane

Larry Guth, Alex Iosevich, Yumeng Ou, Hong Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

If E⊂ R² is a compact set of Hausdorff dimension greater than 5 / 4, we prove that there is a point x∈ E so that the set of distances { | x- y| } _y _∈ _E has positive Lebesgue measure.

Original language	English (US)
Pages (from-to)	779-830
Number of pages	52
Journal	Inventiones Mathematicae
Volume	219
Issue number	3
DOIs	https://doi.org/10.1007/s00222-019-00917-x
State	Published - Mar 1 2020

ASJC Scopus subject areas

General Mathematics

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On Falconer’s distance set problem in the plane

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