Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913340372025344 |
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| author | Cordero-Misteli, Santiago Franz, Giada |
| author_facet | Cordero-Misteli, Santiago Franz, Giada |
| contents | Given a compact Riemannian manifold, of dimension between 3 and 7, with boundary, we adapt Song's method in Song (2023) to the free boundary case to show that the Morse index of a free boundary minimal hypersurface grows linearly with the sum of its Betti numbers, where the constant of growth depends on the area of the free boundary minimal hypersurface in question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02105 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments Cordero-Misteli, Santiago Franz, Giada Differential Geometry Given a compact Riemannian manifold, of dimension between 3 and 7, with boundary, we adapt Song's method in Song (2023) to the free boundary case to show that the Morse index of a free boundary minimal hypersurface grows linearly with the sum of its Betti numbers, where the constant of growth depends on the area of the free boundary minimal hypersurface in question. |
| title | Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2206.02105 |