Equilateral dimension of the planar Banach--Mazur compactum
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908754270748672 |
|---|---|
| author | Kobos, Tomasz Swanepoel, Konrad |
| author_facet | Kobos, Tomasz Swanepoel, Konrad |
| contents | We prove that there are arbitrarily large equilateral sets of planar and symmetric convex bodies in the Banach--Mazur distance. The order of the size of these $d$-equilateral sets asymptotically matches the bounds of the size of maximum-size $d$-separated sets (determined by Bronstein in 1978), showing that our construction is essentially optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilateral dimension of the planar Banach--Mazur compactum Kobos, Tomasz Swanepoel, Konrad Metric Geometry Functional Analysis Primary 52A10. Secondary 46B04, 46B20, 52A22 We prove that there are arbitrarily large equilateral sets of planar and symmetric convex bodies in the Banach--Mazur distance. The order of the size of these $d$-equilateral sets asymptotically matches the bounds of the size of maximum-size $d$-separated sets (determined by Bronstein in 1978), showing that our construction is essentially optimal. |
| title | Equilateral dimension of the planar Banach--Mazur compactum |
| topic | Metric Geometry Functional Analysis Primary 52A10. Secondary 46B04, 46B20, 52A22 |
| url | https://arxiv.org/abs/2503.21478 |