Spectral splitting theorem and ends of minimal hypersurfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909043911557120 |
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| author | Hong, Han Wang, Gaoming |
| author_facet | Hong, Han Wang, Gaoming |
| contents | In this paper, we give a new proof of the splitting theorem on manifolds with nonnegative spectral Ricci curvature proved in [APX24, CMMR24, HW26]. Furthermore, by constructing weighted minimizing geodesics at infinity, we show that minimal hypersurfaces with finite index in manifolds with nonnegative biRic curvature must have finite ends, generalizing the result of Li-Wang [LW04] on manifolds with nonnegative sectional curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14931 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral splitting theorem and ends of minimal hypersurfaces Hong, Han Wang, Gaoming Differential Geometry In this paper, we give a new proof of the splitting theorem on manifolds with nonnegative spectral Ricci curvature proved in [APX24, CMMR24, HW26]. Furthermore, by constructing weighted minimizing geodesics at infinity, we show that minimal hypersurfaces with finite index in manifolds with nonnegative biRic curvature must have finite ends, generalizing the result of Li-Wang [LW04] on manifolds with nonnegative sectional curvature. |
| title | Spectral splitting theorem and ends of minimal hypersurfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.14931 |