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arXiv · 2301.04645

Vertical projections in the Heisenberg group for sets of dimension greater than 3

Terence L. J. Harris
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Abstract

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 F\"assler 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.

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Terence L. J. Harris. 2023-01-11. Vertical projections in the Heisenberg group for sets of dimension greater than 3. https://doi.org/10.1512/iumj.2025.74.60272

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