Dvoretzky-type theorem for Ahlfors regular spaces

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It is proved that for any 0 < β < α, any bounded Ahlfors α-regular space contains a β-regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most O(α/(α − β)). The bound on the distortion is asymptotically tight when β → α. The main tool used in the proof is a regular form of the ultrametric skeleton theorem.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalStudia Mathematica
Issue number1
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2023.


  • Ahlfors regular spaces
  • Dvoretzky-type theorems
  • Hausdorff dimension
  • biLipschitz embeddings
  • metric Ramsey theory
  • ultrametric skeleton


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