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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/2503.19297 |
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| _version_ | 1866910892296241152 |
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| author | Lai, Junqi Wei, Guoxin |
| author_facet | Lai, Junqi Wei, Guoxin |
| contents | Brendle proved Lawson conjecture about minimal embedded torus in the round three-dimensional sphere. Carlotto and Schulz constructed a minimal embedded three-dimensional hypertorus in the round four-dimensional sphere and conjectured that their hypertorus is a unique minimal embedded three-dimensional hypertorus in the round four-dimensional sphere. In this paper, we construct two different constant mean curvature embedded $(2n-1)$-dimensional hypertori (that is, topological type \(\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1\)) which have the same negative mean curvature \(H\) in the round $2n$-dimensional sphere \(\mathbb{S}^{2n}(1)\) . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedded constant mean curvature hypertori in the $2n$-sphere Lai, Junqi Wei, Guoxin Differential Geometry Brendle proved Lawson conjecture about minimal embedded torus in the round three-dimensional sphere. Carlotto and Schulz constructed a minimal embedded three-dimensional hypertorus in the round four-dimensional sphere and conjectured that their hypertorus is a unique minimal embedded three-dimensional hypertorus in the round four-dimensional sphere. In this paper, we construct two different constant mean curvature embedded $(2n-1)$-dimensional hypertori (that is, topological type \(\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1\)) which have the same negative mean curvature \(H\) in the round $2n$-dimensional sphere \(\mathbb{S}^{2n}(1)\) . |
| title | Embedded constant mean curvature hypertori in the $2n$-sphere |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.19297 |