Rationally Convex Surfaces with hyperbolic complex tangencies
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909478605029376 |
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| author | Rizell, Georgios Dimitroglou Lawrence, Mark G. |
| author_facet | Rizell, Georgios Dimitroglou Lawrence, Mark G. |
| contents | We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by handle-bodies, and those that do not have any compact Riemann surfaces attached at all. The fillable examples all live in the round sphere and are unknotted, while the non-fillable examples can moreover be produced in several different smooth isotopy classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rationally Convex Surfaces with hyperbolic complex tangencies Rizell, Georgios Dimitroglou Lawrence, Mark G. Symplectic Geometry Complex Variables 32E20, 53D12 We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by handle-bodies, and those that do not have any compact Riemann surfaces attached at all. The fillable examples all live in the round sphere and are unknotted, while the non-fillable examples can moreover be produced in several different smooth isotopy classes. |
| title | Rationally Convex Surfaces with hyperbolic complex tangencies |
| topic | Symplectic Geometry Complex Variables 32E20, 53D12 |
| url | https://arxiv.org/abs/2502.03357 |