{"title":"Simplices in thin subsets of Euclidean spaces","authors":"Alex Iosevich, Akos Magyar","doi":"10.2140/apde.2023.16.1485","DOIUrl":null,"url":null,"abstract":"Let $\\De$ be a non-degenerate simplex on $k$ vertices. We prove that there exists a threshold $s_k<k$ such that any set $A\\subs \\R^k$ of Hausdorff dimension $dim\\,A\\geq s_k$ necessarily contains a similar copy of the simplex $\\De$.","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":"1 1","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis & PDE","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/apde.2023.16.1485","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 9
Abstract
Let $\De$ be a non-degenerate simplex on $k$ vertices. We prove that there exists a threshold $s_k
期刊介绍:
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