Construction of a curved Kakeya set
Abstract We construct a compact set in of measure 0 containing a piece of a parabola of every aperture between 1 and 2. As a consequence, we improve lower bounds for the ‐ norm of the corresponding maximal operator for a range of . Moreover, our construction can be generalised from parabolas to a family of curves satisfying suitable curvature conditions.
Authors
- Tongou Yang (ORCID: https://orcid.org/0000-0003-2511-9991)
- 岳 大塚
Institutions
- Sun Yat-sen University (CN)
- University of California, Los Angeles (US)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2025-05-30
- DOI
- https://doi.org/10.1112/blms.70110
- Primary Topic
- 3D Modeling in Geospatial Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- National Key Research and Development Program of China