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arXiv · 2608.08201

A Study on Kakeya Needle Problem for $(n-1)$-Rectifiable Sets

Wenjuan Li·Hongqiang Wang·Huiju Wang
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Abstract

In this article we study the analog of Kakeya needle problem for $(n-1)$-rectifiable sets in $\mathbb{R}^n$ and construct the related Nikodym type sets. The novelty of our approach lies in combining three ingredients: the two-dimensional Venetian blind-type construction for isometries in $\mathbb{R}^n$; the normal geometry of a $(n-1)$-rectifiable set viewed in the projective setting; and measure estimates of moving $(n-1)$-rectifiable sets by isometries in $\mathbb{R}^n$. Together, these ingredients enable us to move $(n-1)$-rectifiable sets along paths of isometries in $\mathbb{R}^n$ and cover a Lebesgue null set.

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BibTeXRIS

Wenjuan Li, Hongqiang Wang, Huiju Wang. 2026-08-08. A Study on Kakeya Needle Problem for $(n-1)$-Rectifiable Sets. https://arxiv.org/abs/2608.08201

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