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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12877 |
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Table of 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.