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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2110.01139 |
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| _version_ | 1866916412866428928 |
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| author | Lima, Vanderson Menezes, Ana |
| author_facet | Lima, Vanderson Menezes, Ana |
| contents | We prove that every hyperplane passing through the origin in $\rr^{n+1}$ divides an embedded compact free boundary minimal hypersurface of the euclidean $(n+1)$-ball in exactly two connected hypersurfaces. We also show that if a region in the $(n+1)$-ball has mean convex boundary and contains a nullhomologous $(n-1)$-dimensional equatorial disk, then this region is a closed halfball. Our first result gives evidence to a conjecture by Fraser and Li in any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_01139 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A two-piece property for free boundary minimal hypersurfaces in the $(n+1)$-dimensional ball Lima, Vanderson Menezes, Ana Differential Geometry We prove that every hyperplane passing through the origin in $\rr^{n+1}$ divides an embedded compact free boundary minimal hypersurface of the euclidean $(n+1)$-ball in exactly two connected hypersurfaces. We also show that if a region in the $(n+1)$-ball has mean convex boundary and contains a nullhomologous $(n-1)$-dimensional equatorial disk, then this region is a closed halfball. Our first result gives evidence to a conjecture by Fraser and Li in any dimension. |
| title | A two-piece property for free boundary minimal hypersurfaces in the $(n+1)$-dimensional ball |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2110.01139 |