Year: 2026
Type: preprint
Abstract: The ultrametric skeleton theorem extracts from every compact metric probability space a subset of ultrametric distortion $O(1/\varepsilon)$ that carries a measure whose balls are controlled by the $(1-\varepsilon)$-power of the original measure on dilated concentric balls. We prove a two-sided version for arbitrary compact metric spaces: for every ball centered on the skeleton, the skeleton measure also has a lower bound in terms of the original measure on a smaller nonconcentric ball contained in it. We also give a short proof of the original skeleton theorem and improve the dilation of its control balls from $\exp(O(1/\varepsilon^2))$ to $O(1/\varepsilon)$.
Source: arXiv (Cornell University)
Author: Mendel, Manor
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170045162
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