On uniqueness of free boundary minimal annuli in geodesic balls of $\mathbb{S}^3_+$ and $\mathbb{H}^3$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915695702310912 |
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| author | Lima, César |
| author_facet | Lima, César |
| contents | We consider $Σ$ an embedded free boundary minimal annulus in a geodesic ball in the round hemisphere $\mathbb{S}^3_+$ or in the hyperbolic space $\mathbb{H}^3$. Under the hypothesis of invariance due to an antipodal map on the geodesic ball and using the fact that this surface satisfies the Steklov problem with frequency, we prove that $Σ$ is congruent to a critical rotational annulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On uniqueness of free boundary minimal annuli in geodesic balls of $\mathbb{S}^3_+$ and $\mathbb{H}^3$ Lima, César Differential Geometry We consider $Σ$ an embedded free boundary minimal annulus in a geodesic ball in the round hemisphere $\mathbb{S}^3_+$ or in the hyperbolic space $\mathbb{H}^3$. Under the hypothesis of invariance due to an antipodal map on the geodesic ball and using the fact that this surface satisfies the Steklov problem with frequency, we prove that $Σ$ is congruent to a critical rotational annulus. |
| title | On uniqueness of free boundary minimal annuli in geodesic balls of $\mathbb{S}^3_+$ and $\mathbb{H}^3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.16763 |