{"title":"欧几里得空间的稀疏子集中的单形","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":"{\"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}","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}
期刊介绍:
APDE aims to be the leading specialized scholarly publication in mathematical analysis. The full editorial board votes on all articles, accounting for the journal’s exceptionally high standard and ensuring its broad profile.