English

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 Rd\mathbb{R}^d with d2d \geq 2. 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.

Keywords

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}
}
R2 v1 2026-07-01T03:30:21.622Z