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

Terence L. J. Harris

Published 2022-03-21Version 1

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 for sets $A$ with $1< \dim A < 7/2$, and answers a question of F\"assler and Hovila. The approach uses the Euclidean Fourier transform.