Hausdorff dimension of Besicovitch sets of Cantor graphs

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-02-08 DOI:10.1112/mtk.12241

Iqra Altaf, Marianna Csörnyei, Kornélia Héra

引用次数: 0

Abstract

We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets Γ, that is, sets that contain a rotated copy of Γ in each direction. We show that for a large class of Cantor sets C and Cantor-graphs Γ built on C, the Hausdorff dimension of any Γ-Besicovitch set must be at least , where .

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康托尔图的贝西科维奇集的豪斯多夫维度

我们考虑的是可整型集合 Γ 的平面贝西科维奇集合的豪斯多夫维度，即在每个方向上都包含 Γ 的旋转副本的集合。我们证明，对于一大类 Cantor 集 C 和建立在 C 上的 Cantor 图 Γ，任何 Γ-Besicovitch 集的 Hausdorff 维度必须至少为，其中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.