A one-dimensional planar Besicovitch-type set

2024/12/15 by Iqra Altaf, Altaf, Iqra · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2412.11190

openalex publication_date 2024/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Γ-Besicovitch set is a set which contains a rotated copy of Γ in every direction. Our main result is the construction of a non-trivial 1-rectifiable set Γ in the plane, for which there exists a 1-dimensional Γ-Besicovitch set.

Cited by

• On the Dimension of the CC-geodesic Kakeya sets in the first Heisenberg group

Related

• Hausdorff dimension of Besicovitch sets of Cantor graphs
• The intersection of typical Besicovitch sets with lines
• An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension
• An improved bound on the Minkowski dimension of Besicovitch sets in R³
• On the generalized Hausdorff dimension of Besicovitch sets