A restricted projection problem for fractal sets in $\mathbb{R}^n$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911761249075200 |
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| author | Gan, Shengwen Guo, Shaoming Wang, Hong |
| author_facet | Gan, Shengwen Guo, Shaoming Wang, Hong |
| contents | Let $γ: [-1, 1]\to \mathbb{R}^n$ be a smooth curve that is non-degenerate. Take $m\le n$ and a Borel set $E\subset [0, 1]^n$. We prove that the orthogonal projection of $E$ to the $m$-th order tangent space of $γ$ at $θ\in [-1, 1]$ has Hausdorff dimension $\min\{m, \dim(E)\}$ for almost every $θ\in [-1, 1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09508 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A restricted projection problem for fractal sets in $\mathbb{R}^n$ Gan, Shengwen Guo, Shaoming Wang, Hong Classical Analysis and ODEs Let $γ: [-1, 1]\to \mathbb{R}^n$ be a smooth curve that is non-degenerate. Take $m\le n$ and a Borel set $E\subset [0, 1]^n$. We prove that the orthogonal projection of $E$ to the $m$-th order tangent space of $γ$ at $θ\in [-1, 1]$ has Hausdorff dimension $\min\{m, \dim(E)\}$ for almost every $θ\in [-1, 1]$. |
| title | A restricted projection problem for fractal sets in $\mathbb{R}^n$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2211.09508 |