Remarks on minimal hypersurfaces in gradient shrinking Ricci solitons
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915233756348416 |
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| author | Sun, Yukai Zhu, Guangrui |
| author_facet | Sun, Yukai Zhu, Guangrui |
| contents | In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in gradient Ricci soliton $(M^{n},g,f)$ with scalar curvature $R\geq(n-1)λ$ must have vanished second fundamental form and vanished normal Ricci curvature. For shrinking gradient Ricci solitons with scalar curvature $R\geq(n-1)λ$, the existence of an area-minimizing hypersurface would imply $M$ is splitting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on minimal hypersurfaces in gradient shrinking Ricci solitons Sun, Yukai Zhu, Guangrui Differential Geometry In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in gradient Ricci soliton $(M^{n},g,f)$ with scalar curvature $R\geq(n-1)λ$ must have vanished second fundamental form and vanished normal Ricci curvature. For shrinking gradient Ricci solitons with scalar curvature $R\geq(n-1)λ$, the existence of an area-minimizing hypersurface would imply $M$ is splitting. |
| title | Remarks on minimal hypersurfaces in gradient shrinking Ricci solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.03316 |