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

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

We show that if compact set E ⊂ R d has Hausdorff dimension larger than d 2 + 1 4 , 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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Veröffentlicht in:Mathematische annalen 2021-08, Vol.380 (3-4), p.1215-1231
Hauptverfasser: Du, Xiumin, Iosevich, Alex, Ou, Yumeng, Wang, Hong, Zhang, Ruixiang
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that if compact set E ⊂ R d has Hausdorff dimension larger than d 2 + 1 4 , 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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-021-02170-1