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arXiv · 2203.10915

A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group

Terence L. J. Harris
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Abstract

An improved a.e. lower bound is given for Hausdorff dimension under vertical projections in the first Heisenberg group, with respect to the Carnot-Carath\'eodory metric. This improves the known lower bound, and answers a question of F\"assler and Hovila. The approach uses the Euclidean Fourier transform, Basset's integral formula, and modified Bessel functions of the second kind.

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Terence L. J. Harris. 2022-03-21. A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group. https://doi.org/10.1112/blms.12770

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