Free boundary and capillary minimal surfaces in spherical caps I: Low genus
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911338278682624 |
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| author | Naff, Keaton Zhu, Jonathan J. |
| author_facet | Naff, Keaton Zhu, Jonathan J. |
| contents | This is the first of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls $B_R\subset\mathbb{S}^3$. In this article, we extend our previous half-space intersection properties to warped products, and extend (non-)umbilicity of discs and annuli to capillary minimal surfaces in high codimension. We establish a dual operation relating free boundary and capillary minimal surfaces. These results are discussed in a continuous, unified framework, particularly in relation to uniqueness of minimal annuli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free boundary and capillary minimal surfaces in spherical caps I: Low genus Naff, Keaton Zhu, Jonathan J. Differential Geometry This is the first of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls $B_R\subset\mathbb{S}^3$. In this article, we extend our previous half-space intersection properties to warped products, and extend (non-)umbilicity of discs and annuli to capillary minimal surfaces in high codimension. We establish a dual operation relating free boundary and capillary minimal surfaces. These results are discussed in a continuous, unified framework, particularly in relation to uniqueness of minimal annuli. |
| title | Free boundary and capillary minimal surfaces in spherical caps I: Low genus |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.12877 |