Free boundary minimal surfaces in products of balls
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911222009430016 |
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| author | Choe, Jaigyoung Fraser, Ailana Schoen, Richard |
| author_facet | Choe, Jaigyoung Fraser, Ailana Schoen, Richard |
| contents | In this paper we develop an extremal eigenvalue approach to the problem of construction of free boundary minimal surfaces in the product of Euclidean balls of chosen radii. The extremal problem involves a linear combination of normalized mixed Steklov-Neumann eigenvalues. The problem is motivated by the Schwarz P-surface which is a free boundary minimal surface in a cube. We show that the problem does not have an absolute maximum in the product case. By imposing a finite group of symmetries on both the surface and on the eigenfunctions we construct at least one free boundary minimal surface in a rectangular prism with arbitrary side lengths. We also show that for a genus zero surface with six boundary components and suitable reflection symmetries there is a maximizing metric which can be realized by a free boundary minimal immersion into a product of Euclidean balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free boundary minimal surfaces in products of balls Choe, Jaigyoung Fraser, Ailana Schoen, Richard Differential Geometry 53A10, 58E12, 58C40 In this paper we develop an extremal eigenvalue approach to the problem of construction of free boundary minimal surfaces in the product of Euclidean balls of chosen radii. The extremal problem involves a linear combination of normalized mixed Steklov-Neumann eigenvalues. The problem is motivated by the Schwarz P-surface which is a free boundary minimal surface in a cube. We show that the problem does not have an absolute maximum in the product case. By imposing a finite group of symmetries on both the surface and on the eigenfunctions we construct at least one free boundary minimal surface in a rectangular prism with arbitrary side lengths. We also show that for a genus zero surface with six boundary components and suitable reflection symmetries there is a maximizing metric which can be realized by a free boundary minimal immersion into a product of Euclidean balls. |
| title | Free boundary minimal surfaces in products of balls |
| topic | Differential Geometry 53A10, 58E12, 58C40 |
| url | https://arxiv.org/abs/2510.17729 |