On Hausdorff dimension of radial projections

• Bochen Liu ^[1]
  1. [1] Southern University of Science and Technology, Shenzhen
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 4, 2021, págs. 1307-1319
• Idioma: inglés
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• Resumen

  • 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.