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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.03593 |
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| _version_ | 1866917586787106816 |
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| author | Sewell, Benedict |
| author_facet | Sewell, Benedict |
| contents | In this short note, we show that the inradius of a convex body is comparable to its volume divided by its surface area. We also give a simple formula, in terms of its volume and inradius, that is comparable to the volume of its intersection with the $\varepsilon$-neighbourhood of its boundary, and provide an application of this to self-projective attractors with convex holes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple bounds for the inradius and $\varepsilon$-inner neighbourhood of a convex body Sewell, Benedict Metric Geometry Dynamical Systems 52C07, 28A80 In this short note, we show that the inradius of a convex body is comparable to its volume divided by its surface area. We also give a simple formula, in terms of its volume and inradius, that is comparable to the volume of its intersection with the $\varepsilon$-neighbourhood of its boundary, and provide an application of this to self-projective attractors with convex holes. |
| title | Simple bounds for the inradius and $\varepsilon$-inner neighbourhood of a convex body |
| topic | Metric Geometry Dynamical Systems 52C07, 28A80 |
| url | https://arxiv.org/abs/2401.03593 |