@article{9d2dff64081147b7ba4a1b0d68fb9f87,
title = "On Falconer{\textquoteright}s distance set problem in the plane",
abstract = "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.",
author = "Larry Guth and Alex Iosevich and Yumeng Ou and Hong Wang",
note = "Funding Information: The authors are grateful to the anonymous referees for helpful comments and suggestions. Larry Guth is supported by a Simons Investigator grant. Alex Iosevich is supported in part by the NSA Grant H98230-15-0319. Yumeng Ou is supported in part by NSF-DMS #1854148 (previously #1764454). Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2020",
month = mar,
day = "1",
doi = "10.1007/s00222-019-00917-x",
language = "English (US)",
volume = "219",
pages = "779--830",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer New York",
number = "3",
}