@article{9cbc4183153042fd8f7e4cd5b1a11361,
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",
note = "Funding Information: XD is supported by NSF DMS-1856475. AI was partially supported by NSF HDR TRIPODS 1934985. YO is supported by NSF DMS-1854148. HW is funded by the S.S. Chern Foundation and NSF DMS-1638352. RZ is supported by NSF DMS-1856541. We would like to thank Pablo Shmerkin for pointing out a minor issue in a previous version regarding the pushforward measure under the orthogonal projection. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2021",
month = aug,
doi = "10.1007/s00208-021-02170-1",
language = "English (US)",
volume = "380",
pages = "1215--1231",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "3-4",
}