An improved result for Falconer’s distance set problem in even dimensions

Xiumin Du, Alex Iosevich, Yumeng Ou, Hong Wang, Ruixiang Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We show that if compact set E⊂ Rd has Hausdorff dimension larger than d2+14, where d≥ 4 is an even integer, then the distance set of E has positive Lebesgue measure. This improves the previously best known result towards Falconer’s distance set conjecture in even dimensions.

Original languageEnglish (US)
Pages (from-to)1215-1231
Number of pages17
JournalMathematische Annalen
Volume380
Issue number3-4
DOIs
StatePublished - Aug 2021

ASJC Scopus subject areas

  • Mathematics(all)

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