An improved bound for the dimension of (α, 2α)-Furstenberg sets

被引：9

作者：

Hera, Kornelia ^{[1
]}

Shmerkin, Pablo ^{[2
,3
,4
]}

Yavicoli, Alexia ^{[4
,5
]}

机构：

[1] Univ Chicago, Dept Math, 5734 S Univ Ave, Chicago, IL 60637 USA

[2] Torcuato Tella Univ, Dept Math & Stat, Buenos Aires, DF, Argentina

[3] Consejo Nacl Invest Cient & Tecn, Buenos Aires, DF, Argentina

[4] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

[5] Univ St Andrews, Sch Math & Stat, St Andrews, Fife, Scotland

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2022年 / 38卷 / 01期

基金：

瑞士国家科学基金会; 欧洲研究理事会;

关键词：

Hausdorff dimension; Furstenberg sets; discretized sets; HAUSDORFF DIMENSION; PROJECTIONS; FAMILIES; UNIONS;

D O I：

10.4171/RMI/1281

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that given alpha is an element of (0, 1) there is a constant c = c (alpha) > 0 such that any planar (alpha, 2 alpha)-Furstenberg set has Hausdorff dimension at least 2 alpha + c. This improves several previous bounds, in particular extending a result of Katz-Tao and Bourgain. We follow the Katz-Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps.

引用

页码：295 / 322

页数：28

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