Rigidity of Complete Free Boundary Minimal Hypersurfaces in Convex NNSC Manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916712478146560 |
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| author | Wu, Yujie |
| author_facet | Wu, Yujie |
| contents | We prove that in the unit ball of $\mathbb{R}^4$, there is no complete two-sided stable free boundary immersion. The result follows from a rigidity theorem of complete free boundary minimal hypersurfaces in complete 4-manifolds with non-negative intermediate Ricci curvature, convex boundary and weakly bounded geometry. The method uses warped $θ$-bubble, a generalization of capillary surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of Complete Free Boundary Minimal Hypersurfaces in Convex NNSC Manifolds Wu, Yujie Differential Geometry We prove that in the unit ball of $\mathbb{R}^4$, there is no complete two-sided stable free boundary immersion. The result follows from a rigidity theorem of complete free boundary minimal hypersurfaces in complete 4-manifolds with non-negative intermediate Ricci curvature, convex boundary and weakly bounded geometry. The method uses warped $θ$-bubble, a generalization of capillary surfaces. |
| title | Rigidity of Complete Free Boundary Minimal Hypersurfaces in Convex NNSC Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.20585 |