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

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 F\"assler and Hovila. The approach uses the Euclidean Fourier tr...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Author: Harris, Terence L J
Format: Article
Language:English
Subjects:
Fourier transforms
Lower bounds
Online Access:Get full text
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Summary: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 F\"assler and Hovila. The approach uses the Euclidean Fourier transform, Basset's integral formula, and modified Bessel functions of the second kind.
ISSN:2331-8422
DOI:10.48550/arxiv.2203.10915