SIMPLICES IN THIN SUBSETS OF EUCLIDEAN SPACES

被引：2

作者：

Iosevich, Alex ^{[1
]}

Magyar, Akos ^{[2
]}

机构：

[1] Univ Rochester, Dept Math, Rochester, NY 14627 USA

[2] Univ Georgia, Dept Math, Athens, GA USA

来源：

ANALYSIS & PDE | 2023年 / 16卷 / 07期

基金：

美国国家科学基金会;

关键词：

simplexes; Hausdorff dimension; graphs; SETS; DENSITY;

D O I：

10.2140/apde.2023.16.1485

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be a nondegenerate simplex on k vertices. We prove that there exists a threshold s(k) < k such that any set A subset of R(k )of Hausdorff dimension dim A > s(k )necessarily contains a similar copy of the simplex Delta.

引用

页码：1485 / 1496

页数：13

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