Resumen de On Hausdorff dimension of radial projections

Bochen Liu

• For any x∈Rd, d≥2, denote by πx:Rd∖{x}→Sd−1 the radial projectionπx(y)=y−x|y−x|⋅ Given a Borel set E⊂Rd with dimHE≤d−1, in this paper we investigate for how many x∈Rd the radial projection πx preserves the Hausdorff dimension of E, namely whether dimHπx(E)=dimHE. We develop a general framework to link πx(E), x∈F, and πy(F), y∈E, for any Borel set F⊂Rd. In particular, this allows us to apply Orponen's estimate on visibility to study whether dimHπx(E)=dimHE for some x∈F.