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arXiv · 2106.11737

Dvoretzky-type theorem for Ahlfors regular spaces

Manor Mendel
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Abstract

It is proved that for any $0<\beta<\alpha$, 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.

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Manor Mendel. 2021-06-22. Dvoretzky-type theorem for Ahlfors regular spaces. https://doi.org/10.4064/sm210629-2-2

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