Attainable forms of intermediate dimensions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914907286405120 |
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| author | Banaji, Amlan Rutar, Alex |
| author_facet | Banaji, Amlan Rutar, Alex |
| contents | The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given function $h(θ)$ to be realized as the intermediate dimensions of a bounded subset of $\mathbb{R}^d$. This condition is a straightforward constraint on the Dini derivatives of $h(θ)$, which we prove is sharp using a homogeneous Moran set construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_14678 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Attainable forms of intermediate dimensions Banaji, Amlan Rutar, Alex Metric Geometry Classical Analysis and ODEs Dynamical Systems 28A78, 28A80 The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given function $h(θ)$ to be realized as the intermediate dimensions of a bounded subset of $\mathbb{R}^d$. This condition is a straightforward constraint on the Dini derivatives of $h(θ)$, which we prove is sharp using a homogeneous Moran set construction. |
| title | Attainable forms of intermediate dimensions |
| topic | Metric Geometry Classical Analysis and ODEs Dynamical Systems 28A78, 28A80 |
| url | https://arxiv.org/abs/2111.14678 |