Fast repetitivity in non-rectifiable Delone sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912682338156544 |
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| author | Bhat, Ashwin Dymond, Michael |
| author_facet | Bhat, Ashwin Dymond, Michael |
| contents | We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $\mathbb{R}^d$ with $d \geq 2$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast repetitivity in non-rectifiable Delone sets Bhat, Ashwin Dymond, Michael Metric Geometry Discrete Mathematics Functional Analysis 51F23, 52C23, 51M05, 28A33, 30L05, 26B10 We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $\mathbb{R}^d$ with $d \geq 2$. 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. |
| title | Fast repetitivity in non-rectifiable Delone sets |
| topic | Metric Geometry Discrete Mathematics Functional Analysis 51F23, 52C23, 51M05, 28A33, 30L05, 26B10 |
| url | https://arxiv.org/abs/2506.19114 |