On Falconer’s distance set problem in the plane

Larry Guth, Alex Iosevich, Yumeng Ou, Hong Wang

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)779-830
Number of pages52
JournalInventiones Mathematicae
Issue number3
StatePublished - Mar 1 2020

ASJC Scopus subject areas

  • General Mathematics


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