Twisted embeddings of tori have small extrinsic systole
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910129317740544 |
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| author | Vasudevan, Sahana |
| author_facet | Vasudevan, Sahana |
| contents | We prove a type of systolic inequality for embeddings of $T^2$ in $\mathbb{R}^3$. In particular, a highly twisted $T^2$ embedded in $\mathbb{R}^3$ must contain a non-contractible loop of small $\mathbb{R}^3$-diameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted embeddings of tori have small extrinsic systole Vasudevan, Sahana Differential Geometry Metric Geometry We prove a type of systolic inequality for embeddings of $T^2$ in $\mathbb{R}^3$. In particular, a highly twisted $T^2$ embedded in $\mathbb{R}^3$ must contain a non-contractible loop of small $\mathbb{R}^3$-diameter. |
| title | Twisted embeddings of tori have small extrinsic systole |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2507.23766 |