Hausdorff dimension of Besicovitch sets of Cantor graphs

被引：0

作者：

Altaf, Iqra ^{[1
]}

Csoernyei, Marianna ^{[1
]}

Hera, Kornelia ^{[2
,3
]}

机构：

[1] Univ Chicago, Dept Math, Chicago, IL USA

[2] Univ Bonn, Math Inst, Bonn, Germany

[3] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

MATHEMATIKA | 2024年 / 70卷 / 02期

关键词：

D O I：

10.1112/mtk.12241

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets Gamma, that is, sets that contain a rotated copy of Gamma in each direction. We show that for a large class of Cantor sets C and Cantor-graphs Gamma built on C, the Hausdorff dimension of any Gamma-Besicovitch set must be at least min(2-s2,1s)$\min (2-s<^>2,\frac{1}{s})$, where s=dimC$s={\rm dim}\, C$.

引用

页数：16

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