Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.16223 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913979365851136 |
|---|---|
| author | Lee, Andrew Colbert, Cory H. |
| author_facet | Lee, Andrew Colbert, Cory H. |
| contents | We consider the embedding function $c_b(a)$ describing the problem of symplectically embedding an ellipsoid $E(1,a)$ into the smallest possible scaling by $λ>1$ of the polydisc $P(1,b)$. In particular, we calculate rigid-flexible values, i.e. the minimum $a$ such that for $E(1,a')$ with $a'>a$, the embedding problem is determined only by volume. For $1<b<2$ we find that these values vary piecewise smoothly outside the discrete set $b\in\left(\frac{n+1}{n}\right)^2$. As Jin and Lee analyze packing stability in the caes $b>2$, our results complete the story outside of a discrete set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16223 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigid-flexible values for symplectic embeddings of four-dimensional ellipsoids into almost-cubes Lee, Andrew Colbert, Cory H. Symplectic Geometry We consider the embedding function $c_b(a)$ describing the problem of symplectically embedding an ellipsoid $E(1,a)$ into the smallest possible scaling by $λ>1$ of the polydisc $P(1,b)$. In particular, we calculate rigid-flexible values, i.e. the minimum $a$ such that for $E(1,a')$ with $a'>a$, the embedding problem is determined only by volume. For $1<b<2$ we find that these values vary piecewise smoothly outside the discrete set $b\in\left(\frac{n+1}{n}\right)^2$. As Jin and Lee analyze packing stability in the caes $b>2$, our results complete the story outside of a discrete set. |
| title | Rigid-flexible values for symplectic embeddings of four-dimensional ellipsoids into almost-cubes |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2402.16223 |