On Hausdorff dimension of radial projections
Bochen Liu
Southern University of Science and Technology, Shenzhen, China
Abstract
For any , , denote by the radial projection
Given a Borel set with , in this paper we investigate for how many the radial projection preserves the Hausdorff dimension of , namely whether . We develop a general framework to link , , and , , for any Borel set . In particular, this allows us to apply Orponen's estimate on visibility to study whether for some . More precisely, we show
for any Borel set \n{with} . This improves the Peres–Schlag bound when , and it is optimal at the endpoint .
Cite this article
Bochen Liu, On Hausdorff dimension of radial projections. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1307–1319
DOI 10.4171/RMI/1227