Index and nullity of minimal surface doublings, I
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911308494929920 |
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| author | Kapouleas, Nikolaos Zou, Jiahua |
| author_facet | Kapouleas, Nikolaos Zou, Jiahua |
| contents | We prove that for any large enough $m \in\mathbb{N}$, the genus $γ=m+1$ equator-poles minimal surface doubling of the equatorial two-sphere $Σ^0 = \mathbb{S}^2_{\mathrm{eq}}$ in the round three-sphere $\mathbb{S}^3$, which has two catenoidal bridges at the poles and $m$ bridges equidistributed along the equatorial circle $\mathscr{C}$ of $Σ^0 $ and was discovered in earlier work of Kapouleas, has index $2γ+5=2m+7$ and nullity $6$, and so it has no exceptional Jacobi fields and is $C^1$-isolated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_07734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Index and nullity of minimal surface doublings, I Kapouleas, Nikolaos Zou, Jiahua Differential Geometry 53A05, 53C21 We prove that for any large enough $m \in\mathbb{N}$, the genus $γ=m+1$ equator-poles minimal surface doubling of the equatorial two-sphere $Σ^0 = \mathbb{S}^2_{\mathrm{eq}}$ in the round three-sphere $\mathbb{S}^3$, which has two catenoidal bridges at the poles and $m$ bridges equidistributed along the equatorial circle $\mathscr{C}$ of $Σ^0 $ and was discovered in earlier work of Kapouleas, has index $2γ+5=2m+7$ and nullity $6$, and so it has no exceptional Jacobi fields and is $C^1$-isolated. |
| title | Index and nullity of minimal surface doublings, I |
| topic | Differential Geometry 53A05, 53C21 |
| url | https://arxiv.org/abs/2512.07734 |