A congruence theorem for compact embedded hypersurfaces in $\mathbb{S}^{n+1}_+$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917867736268800 |
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| author | Freitas, Allan Guimarães, Felippe |
| author_facet | Freitas, Allan Guimarães, Felippe |
| contents | We prove a codimension reduction and congruence theorem for compact $n$-dimensional submanifolds of $\mathbb{S}^{n+p}$ that admit a mean convex isometric embedding into $\mathbb{S}^{n+1}_+$ using a Reilly type formula for space forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A congruence theorem for compact embedded hypersurfaces in $\mathbb{S}^{n+1}_+$ Freitas, Allan Guimarães, Felippe Differential Geometry 53A07, 53C42 We prove a codimension reduction and congruence theorem for compact $n$-dimensional submanifolds of $\mathbb{S}^{n+p}$ that admit a mean convex isometric embedding into $\mathbb{S}^{n+1}_+$ using a Reilly type formula for space forms. |
| title | A congruence theorem for compact embedded hypersurfaces in $\mathbb{S}^{n+1}_+$ |
| topic | Differential Geometry 53A07, 53C42 |
| url | https://arxiv.org/abs/2404.12197 |