On Hausdorff dimension of radial projections

  • Bochen Liu

    Southern University of Science and Technology, Shenzhen, China
On Hausdorff dimension of radial projections cover

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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