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

Xiumin Du; Alex Iosevich; Yumeng Ou; Hong Wang; Ruixiang Zhang

doi:10.1007/s00208-021-02170-1

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

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

Mathematics

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

Abstract

We show that if compact set E⊂ R^d 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 language	English (US)
Pages (from-to)	1215-1231
Number of pages	17
Journal	Mathematische Annalen
Volume	380
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02170-1
State	Published - Aug 2021

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-021-02170-1

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title = "An improved result for Falconer{\textquoteright}s distance set problem in even dimensions",

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{\textquoteright}s distance set conjecture in even dimensions.",

author = "Xiumin Du and Alex Iosevich and Yumeng Ou and Hong Wang and Ruixiang Zhang",

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AU - Zhang, Ruixiang

PY - 2021/8

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AB - 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.

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

Abstract

ASJC Scopus subject areas

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