Complete minimal surfaces with Cantor ends in minimally convex domains
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912075477942272 |
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| author | Alarcon, Antonio |
| author_facet | Alarcon, Antonio |
| contents | We survey the recent history of the conformal Calabi-Yau problem consisting in determining the complex structures admitted by complete bounded minimal surfaces in $\mathbb{R}^3$. Moreover, we prove that for any minimally convex domain $Ω$ in $\mathbb{R}^3$ and any compact Riemann surface $R$ there is a Cantor set $C$ in $R$ whose complement $R\setminus C$ is the complex structure of a complete proper minimal surface in $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete minimal surfaces with Cantor ends in minimally convex domains Alarcon, Antonio Differential Geometry We survey the recent history of the conformal Calabi-Yau problem consisting in determining the complex structures admitted by complete bounded minimal surfaces in $\mathbb{R}^3$. Moreover, we prove that for any minimally convex domain $Ω$ in $\mathbb{R}^3$ and any compact Riemann surface $R$ there is a Cantor set $C$ in $R$ whose complement $R\setminus C$ is the complex structure of a complete proper minimal surface in $Ω$. |
| title | Complete minimal surfaces with Cantor ends in minimally convex domains |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.13687 |