A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group
Classical Analysis and ODEs
2023-11-02 v6 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2203.10915,
title = {A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group},
author = {Terence L. J. Harris},
journal= {arXiv preprint arXiv:2203.10915},
year = {2023}
}
Comments
16 pages. V2: Some minor refinements to Lemma 3.1, and added some background on Bessel functions. V3: Minor corrections V4: Minor corrections and added some concluding remarks. V5: Simplified proof of Lemma 3.2. V6: Minor corrections. Accepted version