Vertical projections in the Heisenberg group for sets of dimension greater than 3
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916926123409408 |
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| author | Harris, Terence L. J. |
| author_facet | Harris, Terence L. J. |
| contents | It is shown that vertical projections in the Heisenberg group of sets of dimension strictly greater than 3 almost surely have positive area. The proof uses the point-plate incidence method introduced by Fässler and Orponen, and also uses a similar approach to a recent maximal inequality of Zahl for fractal families of tubes. It relies on the endpoint trilinear Kakeya inequality in $\mathbb{R}^3$. Some related results are given on generic intersections with horizontal lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04645 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vertical projections in the Heisenberg group for sets of dimension greater than 3 Harris, Terence L. J. Classical Analysis and ODEs 28A78, 28A80 It is shown that vertical projections in the Heisenberg group of sets of dimension strictly greater than 3 almost surely have positive area. The proof uses the point-plate incidence method introduced by Fässler and Orponen, and also uses a similar approach to a recent maximal inequality of Zahl for fractal families of tubes. It relies on the endpoint trilinear Kakeya inequality in $\mathbb{R}^3$. Some related results are given on generic intersections with horizontal lines. |
| title | Vertical projections in the Heisenberg group for sets of dimension greater than 3 |
| topic | Classical Analysis and ODEs 28A78, 28A80 |
| url | https://arxiv.org/abs/2301.04645 |