Higher genus Angel surfaces
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908937887940608 |
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| author | Bardhan, Rivu Biswas, Indranil Fujimori, Shoichi Kumar, Pradip |
| author_facet | Bardhan, Rivu Biswas, Indranil Fujimori, Shoichi Kumar, Pradip |
| contents | We prove the existence of complete minimal surfaces in $\mathbb{R}^3$ of arbitrary genus $p\, \ge\, 1$ and least total absolute curvature with precisely two ends -- one catenoidal and one Enneper-type -- thereby solving, affirmatively, a problem posed by Fujimori and Shoda. These surfaces, which are called \emph{Angel surfaces}, generalize some examples numerically constructed earlier by Weber. The construction of these minimal surfaces involves extending the orthodisk method developed by Weber and Wolf \cite{weber2002teichmuller}. A central idea in our construction is the notion of \emph{partial symmetry}, which enables us to introduce controlled symmetry into the surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03925 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher genus Angel surfaces Bardhan, Rivu Biswas, Indranil Fujimori, Shoichi Kumar, Pradip Differential Geometry 53A10, 49Q05, 53C42, 30F60 We prove the existence of complete minimal surfaces in $\mathbb{R}^3$ of arbitrary genus $p\, \ge\, 1$ and least total absolute curvature with precisely two ends -- one catenoidal and one Enneper-type -- thereby solving, affirmatively, a problem posed by Fujimori and Shoda. These surfaces, which are called \emph{Angel surfaces}, generalize some examples numerically constructed earlier by Weber. The construction of these minimal surfaces involves extending the orthodisk method developed by Weber and Wolf \cite{weber2002teichmuller}. A central idea in our construction is the notion of \emph{partial symmetry}, which enables us to introduce controlled symmetry into the surface. |
| title | Higher genus Angel surfaces |
| topic | Differential Geometry 53A10, 49Q05, 53C42, 30F60 |
| url | https://arxiv.org/abs/2509.03925 |