Periodicity characterization by capacities for star-shaped domains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912726186459136 |
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| author | Gutt, Jean Ramos, Vinicius G. B. Tanny, Shira |
| author_facet | Gutt, Jean Ramos, Vinicius G. B. Tanny, Shira |
| contents | We complete the spectral characterization of Besse and Zoll Reeb flows on the standard contact sphere $S^{2n-1}$ initiated by Ginzburg-Gürel-Mazzucchelli. Roughly speaking, it states that a Reeb flow on the boundary of any star-shaped domain in $\mathbb{R}^{2n}$ is Besse if and only if it has $n$ coinciding Ekeland-Hofer capacities, and that it is Zoll if and only if the first $n$ capacities coincide. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_18401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodicity characterization by capacities for star-shaped domains Gutt, Jean Ramos, Vinicius G. B. Tanny, Shira Symplectic Geometry 53D10, 37J46, 53D40 We complete the spectral characterization of Besse and Zoll Reeb flows on the standard contact sphere $S^{2n-1}$ initiated by Ginzburg-Gürel-Mazzucchelli. Roughly speaking, it states that a Reeb flow on the boundary of any star-shaped domain in $\mathbb{R}^{2n}$ is Besse if and only if it has $n$ coinciding Ekeland-Hofer capacities, and that it is Zoll if and only if the first $n$ capacities coincide. |
| title | Periodicity characterization by capacities for star-shaped domains |
| topic | Symplectic Geometry 53D10, 37J46, 53D40 |
| url | https://arxiv.org/abs/2511.18401 |