A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group
arXiv:2203.10915 · doi:10.1112/blms.12770
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-Carathéodory metric. This improves the known lower bound, and answers a question of Fässler and Hovila. The approach uses the Euclidean Fourier transform, Basset's integral formula, and modified Bessel functions of the second kind.
arXiv comment16 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