On closed characteristics of minimal action on a convex three-sphere
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909412359143424 |
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| author | Abbondandolo, Alberto Edtmair, Oliver Kang, Jungsoo |
| author_facet | Abbondandolo, Alberto Edtmair, Oliver Kang, Jungsoo |
| contents | We prove that every closed characteristic of minimal action on the boundary of a uniformly convex domain in $\R^4$ bounds a disk-like global surface of section. A corollary is that the cylindrical symplectic capacity of a convex body in $\R^4$ coincides with the minimal action of a closed generalized characteristic on its boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On closed characteristics of minimal action on a convex three-sphere Abbondandolo, Alberto Edtmair, Oliver Kang, Jungsoo Symplectic Geometry Dynamical Systems 37J39, 37C27, 53D40 We prove that every closed characteristic of minimal action on the boundary of a uniformly convex domain in $\R^4$ bounds a disk-like global surface of section. A corollary is that the cylindrical symplectic capacity of a convex body in $\R^4$ coincides with the minimal action of a closed generalized characteristic on its boundary. |
| title | On closed characteristics of minimal action on a convex three-sphere |
| topic | Symplectic Geometry Dynamical Systems 37J39, 37C27, 53D40 |
| url | https://arxiv.org/abs/2412.01777 |