The Calabi-Yau problem for minimal surfaces with Cantor ends
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917981212114944 |
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| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in $\mathbb R^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into $\mathbb C^n$ with $n\ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions in any self-dual or anti-self-dual Einstein four-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07601 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Calabi-Yau problem for minimal surfaces with Cantor ends Forstneric, Franc Differential Geometry Complex Variables Primary 53A10. Secondary 32B15 We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in $\mathbb R^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into $\mathbb C^n$ with $n\ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions in any self-dual or anti-self-dual Einstein four-manifold. |
| title | The Calabi-Yau problem for minimal surfaces with Cantor ends |
| topic | Differential Geometry Complex Variables Primary 53A10. Secondary 32B15 |
| url | https://arxiv.org/abs/2202.07601 |