A sharp inequality between scalar curvature and the bottom spectrum on complete manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910062590558208 |
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| author | Liu, Daoqiang |
| author_facet | Liu, Daoqiang |
| contents | In this paper, we generalize the notion of relative $\widehat{A}$-cowaist, introduced by Cecchini and Zeidler, and establish a sharp inequality linking it to scalar curvature and the bottom spectrum. This yields a number of geometric applications, including progress on the generalized Geroch conjecture and estimates for the bottom spectrum under scalar curvature lower bounds. Our approach is based on deformed Dirac operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A sharp inequality between scalar curvature and the bottom spectrum on complete manifolds Liu, Daoqiang Differential Geometry In this paper, we generalize the notion of relative $\widehat{A}$-cowaist, introduced by Cecchini and Zeidler, and establish a sharp inequality linking it to scalar curvature and the bottom spectrum. This yields a number of geometric applications, including progress on the generalized Geroch conjecture and estimates for the bottom spectrum under scalar curvature lower bounds. Our approach is based on deformed Dirac operators. |
| title | A sharp inequality between scalar curvature and the bottom spectrum on complete manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.20864 |