Radial projections along chains

Abstract

We state strong Marstrand properties for two related families of fractals in Heisenberg groups H d : limit sets of Schottky groups in good position, and attractors of self-similar IFS enjoying the open set condition in the quotient H d /Z. For such a fractal X, we show that the dimension of πxX does not depend on x ∈ H d , where πx denotes the radial projection along chains passing through x. This follows from a local entropy averages argument due to Hochman and Shmerkin.