Free boundary and capillary minimal surfaces in spherical caps II: Low energy
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914218024894464 |
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| author | Zhu, Jonathan J. |
| author_facet | Zhu, Jonathan J. |
| contents | This is the second 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 find monotonicity formulae which imply that capillary minimal surfaces maximise a certain modified energy in their conformal orbit (preserving $B_R$). In the hemisphere, this energy is precisely the capillary energy. We also prove a partial characterisation by index for capillary minimal surfaces in the hemisphere, analogous to Urbano's characterisation of the Clifford torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free boundary and capillary minimal surfaces in spherical caps II: Low energy Zhu, Jonathan J. Differential Geometry This is the second 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 find monotonicity formulae which imply that capillary minimal surfaces maximise a certain modified energy in their conformal orbit (preserving $B_R$). In the hemisphere, this energy is precisely the capillary energy. We also prove a partial characterisation by index for capillary minimal surfaces in the hemisphere, analogous to Urbano's characterisation of the Clifford torus. |
| title | Free boundary and capillary minimal surfaces in spherical caps II: Low energy |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.20857 |