On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán
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| Format: | Preprint |
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2025
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| _version_ | 1866917101883621376 |
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| author | Brendle, Simon Tsiamis, Raphael Wang, Yipeng |
| author_facet | Brendle, Simon Tsiamis, Raphael Wang, Yipeng |
| contents | We consider fill-ins of spin manifolds with scalar curvature bounded by $-n(n-1)$. Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the hyperspherical radius. We observe that the inequality conjectured by Gromov follows by combining an inequality of Hijazi-Montiel-Roldán for the first Dirac eigenvalue with a recent theorem of Bär. Moreover, we give an alternative proof of the Hijazi-Montiel-Roldán inequality based on the work of Bär and Bär-Ballmann. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán Brendle, Simon Tsiamis, Raphael Wang, Yipeng Differential Geometry 53C20, 53C21, 53C27 We consider fill-ins of spin manifolds with scalar curvature bounded by $-n(n-1)$. Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the hyperspherical radius. We observe that the inequality conjectured by Gromov follows by combining an inequality of Hijazi-Montiel-Roldán for the first Dirac eigenvalue with a recent theorem of Bär. Moreover, we give an alternative proof of the Hijazi-Montiel-Roldán inequality based on the work of Bär and Bär-Ballmann. |
| title | On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán |
| topic | Differential Geometry 53C20, 53C21, 53C27 |
| url | https://arxiv.org/abs/2510.17780 |