A non-sticky Kakeya set of Lebesgue measure zero

[2506.18142] A non-sticky Kakeya set of Lebesgue measure zero Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Classical Analysis and ODEs arXiv:2506.18142 (math) [Submitted on 22 Jun 2025 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: A non-sticky Kakeya set of Lebesgue measure zero Authors: Chun-Kit Lai , Adeline E. Wong View a PDF of the paper titled A non-sticky Kakeya set of Lebesgue measure zero, by Chun-Kit Lai and Adeline E. Wong View PDF HTML (experimental) Abstract: The Kakeya set conjecture in ${\mathbb R} ^3$ was recently resolved by Wang and Zahl. The distinction between sticky and non-sticky Kakeya sets plays an important role in their proof. Although the proof did not require the Kakeya set to be Lebesgue measure zero, measure zero Kakeya sets are the crucial case whose study is required to resolve the conjecture. In this paper, we explicitly construct a non-sticky Kakeya set of Lebesgue measure zero in ${\mathbb R}^2$ (and hence in any dimension). We also construct non-trivial sticky and non-sticky Kakeya sets in high dimension that are not formed by taking the Cartesian product of a 2-dimensional Kakeya set with ${\mathbb R}^{d-2}$, and we verify that both Kakeya sets have Hausdorff dimension $d$. Comments: Minor changes Subjects: Classical Analysis and ODEs (math.CA) ; Metric Geometry (math.MG) Cite as: arXiv:2506.18142 [math.CA] (or arXiv:2506.18142v2 [math.CA] for this version) https://doi.org/10.48550/arXiv.2506.18142 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Chun-Kit Lai [ view email ] [v1] Sun, 22 Jun 2025 19:10:38 UTC (28 KB) [v2] Sat, 15 Aug 2026 06:44:48 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled A non-sticky Kakeya set of Lebesgue measure zero, by Chun-Kit Lai and Adeline E. Wong View PDF HTML (experimental) TeX Source view license Current browse context: math.CA < prev | next > new | recent | 2025-06 Change to browse by: math math.MG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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