PreprintCC BY 4.0arXiv
New bound on the Hausdorff dimension of Kakeya sets in ℝ4
Abstract
We obtain a slight improvement to the trilinear bound of Guth-Zahl by application of Wang-Zahl's resolution of 3-D Kakeya to tubes inside a thickened neighborhood of a variety. This is combined with the planebrush argument of Katz and Zahl to obtain the new bound of 3.073.
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BibTeX
@misc{choudhuri2026bound,
title = {{New bound on the Hausdorff dimension of Kakeya sets in $\mathbbR^4$}},
author = {Mukul Rai Choudhuri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12480},
eprint = {2610.12480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12480},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New bound on the Hausdorff dimension of Kakeya sets in ℝ^4
AU - Mukul Rai Choudhuri
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.12480
UR - https://arxiv.org/abs/2610.12480
AB - We obtain a slight improvement to the trilinear bound of Guth-Zahl by application of Wang-Zahl's resolution of 3-D Kakeya to tubes inside a thickened neighborhood of a variety. This is combined with the planebrush argument of Katz and Zahl to obtain the new bound of 3.073.
ER -