Ultrametric subsets with large Hausdorff dimension

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

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 - 2013

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Hausdorff Dimension
Ultrametric Space
Expander Graphs
Subset
Compact Metric Space
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Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Ultrametric subsets with large Hausdorff dimension. / Mendel, Manor; Naor, Assaf.

In: Inventiones Mathematicae, Vol. 192, No. 1, 2013, p. 1-54.

Research output: Contribution to journalArticle

Mendel, Manor ; Naor, Assaf. / Ultrametric subsets with large Hausdorff dimension. In: Inventiones Mathematicae. 2013 ; Vol. 192, No. 1. pp. 1-54.
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