ON THE MULTIPARAMETER FALCONER DISTANCE PROBLEM

Xiumin Du, Yumeng Ou, Ruixiang Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study an extension of the Falconer distance problem in the multiparameter setting. Given ℓ ≥ 1 and ℝd = ℝd1 × · · · × ℝdℓ, di ≥ 2. For any compact set E ⊂ ℝd with Hausdorff dimension larger than d− min(2di) + 14 if min(di) is even, d− min(2di) + 14 + 4 min(1di) if min(di) is odd, we prove that the multiparameter distance set of E has positive ℓ-dimensional Lebesgue measure. A key ingredient in the proof is a new multiparameter radial projection theorem for fractal measures.

Original languageEnglish (US)
Pages (from-to)4979-5010
Number of pages32
JournalTransactions of the American Mathematical Society
Volume375
Issue number7
DOIs
StatePublished - Jul 1 2022

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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