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