Hyperplane Furstenberg Sets in Higher Dimensions

The hyperplane Furstenberg problem asks how small the Hausdorff dimension of $E\subset\mathbb{R}^n$ can be when a $t$-dimensional family of affine $(n-1)$-dimensional hyperplanes meets $E$ in sets of dimension at least $s$. For $0

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.03504
Primary Topic
Mathematical Dynamics and Fractals
Type
preprint
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preprint

Hyperplane Furstenberg Sets in Higher Dimensions

Peiqi Nie
arXiv (Cornell University)
Mathematical Dynamics and Fractals
preprint

Hyperplane Furstenberg Sets in Higher Dimensions

Peiqi Nie
preprint en

Abstract

The hyperplane Furstenberg problem asks how small the Hausdorff dimension of $E\subset\mathbb{R}^n$ can be when a $t$-dimensional family of affine $(n-1)$-dimensional hyperplanes meets $E$ in sets of dimension at least $s$. For $0

arXiv (Cornell University)
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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Hyperplane Furstenberg Sets in Higher Dimensions — Peiqi Nie · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS