Regular ultrametric skeletons
Metric Geometry
2026-07-20 v1
Abstract
The theorem of Mendel and Naor (2013) associates to every compact metric probability space a large ultrametric subset carrying a probability measure controlled from above on balls by the original measure. Building on Bartal's Ramsey decompositions (2021) and the author's previous proofs of the ultrametric skeleton theorem for doubling spaces (2022, 2023), we prove a regular version for arbitrary compact metric spaces with a linear dilation of the control balls.
Cite
@article{arxiv.2607.18525,
title = {Regular ultrametric skeletons},
author = {Manor Mendel},
journal= {arXiv preprint arXiv:2607.18525},
year = {2026}
}
Comments
15 pages