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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.07016 |
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| _version_ | 1866917125788008448 |
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| author | Kang, Jungsoo |
| author_facet | Kang, Jungsoo |
| contents | The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere $S^{2n-1}$ admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into $\mathbb{R}^{2n}$ under the assumption that minimal periodic Reeb orbits are of Morse-Bott type. We also provide a counterexample when the convexity condition is not satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07016 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the strong Arnold chord conjecture for convex contact forms Kang, Jungsoo Symplectic Geometry The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere $S^{2n-1}$ admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into $\mathbb{R}^{2n}$ under the assumption that minimal periodic Reeb orbits are of Morse-Bott type. We also provide a counterexample when the convexity condition is not satisfied. |
| title | On the strong Arnold chord conjecture for convex contact forms |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2304.07016 |