HAUSDORFF DIMENSION OF PINNED DISTANCE SETS AND THE L2-METHOD

被引：16
作者：
Liu, Bochen [1 ]
机构：
[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 01期
关键词：
Hausdorff dimension; Falconer distance conjecture; pinned distances;
D O I：
10.1090/proc/14740
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that for any compact set E subset of R-2, dim(H)(E) > 1, there exists x is an element of E such that the Hausdorff dimension of the pinned distance set Delta(x) (E) = {vertical bar x - y vertical bar : y is an element of E} is no less than min {4/3 dim(H)(E) - 2/3, 1}. This answers a question recently raised by Guth, Iosevich, Ou, and Wang, as well as improves results of Keleti and Shmerkin.
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页码：333 / 341
页数：9
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