Fast repetitivity in non-rectifiable Delone sets
Metric Geometry
2025-11-04 v3 Discrete Mathematics
Functional Analysis
Abstract
We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space with . We further obtain a close to optimal repetitivity function for such sets. The proof is based on the process of encoding a non-realisable density in a Delone set, due to Burago and Kleiner.
Cite
@article{arxiv.2506.19114,
title = {Fast repetitivity in non-rectifiable Delone sets},
author = {Ashwin Bhat and Michael Dymond},
journal= {arXiv preprint arXiv:2506.19114},
year = {2025}
}