Ultrametric subsets with large Hausdorff dimension

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

It is shown that for every ε∈(0,1), every compact metric space (X,d) has a compact subset S⊆X that embeds into an ultrametric space with distortion O(1/ε), and dimH(S),≥(1-ε)dimH(X) where dimH(·) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.

Original languageEnglish (US)
Pages (from-to)1-54
Number of pages54
JournalInventiones Mathematicae
Volume192
Issue number1
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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