The Gromov-Hausdorff distance between $l^p$-products of metric spaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910036694925312 |
|---|---|
| author | Abdullaev, Emin |
| author_facet | Abdullaev, Emin |
| contents | This paper studies $l^p$-products of metric spaces and provides estimates for the Gromov-Hausdorff distances between them. The case of linear products is considered separately, and sufficient conditions for attainability of the estimates are given for it. Examples of calculating the Gromov-Hausdorff distance between flat tori are given. It is proved that for any metric space $X$ of density $d(X)$, the Gromov-Hausdorff distance between it and its $l^\infty$-product (in which the number of factors corresponds to $d(X)$) is equal to half its diameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Gromov-Hausdorff distance between $l^p$-products of metric spaces Abdullaev, Emin Metric Geometry 51F99 This paper studies $l^p$-products of metric spaces and provides estimates for the Gromov-Hausdorff distances between them. The case of linear products is considered separately, and sufficient conditions for attainability of the estimates are given for it. Examples of calculating the Gromov-Hausdorff distance between flat tori are given. It is proved that for any metric space $X$ of density $d(X)$, the Gromov-Hausdorff distance between it and its $l^\infty$-product (in which the number of factors corresponds to $d(X)$) is equal to half its diameter. |
| title | The Gromov-Hausdorff distance between $l^p$-products of metric spaces |
| topic | Metric Geometry 51F99 |
| url | https://arxiv.org/abs/2603.00796 |