Dvoretzky-type theorem for Ahlfors regular spaces
Tom 268 / 2023
Studia Mathematica 268 (2023), 1-22
MSC: Primary 51F30; Secondary 28A78.
DOI: 10.4064/sm210629-2-2
Opublikowany online: 22 July 2022
Streszczenie
It is proved that for any $0 \lt \beta \lt \alpha $, any bounded Ahlfors $\alpha $-regular space contains a $\beta $-regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most $O(\alpha /(\alpha -\beta ))$. The bound on the distortion is asymptotically tight when $\beta \to \alpha $. The main tool used in the proof is a regular form of the ultrametric skeleton theorem.
