Ultrametric subsets with large Hausdorff dimension

• 成果类型: Article
• 署名作者: Mendel, Manor; Naor, Assaf
• 署名单位: Open University Israel; New York University; Microsoft; University of Washington; University of Washington Seattle
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0402-7
• 发表日期: 2013
• 页码: 1-54
• 关键词: spaces; server; bounds; sets

摘要

It is shown that for every epsilon a(0,1), every compact metric space (X,d) has a compact subset SaS dagger X that embeds into an ultrametric space with distortion O(1/epsilon), and dim(H) (S) >= (1 - epsilon) dim(H) (X), where dim (H) (.) denotes Hausdorff dimension. The above O(1/epsilon) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.