Bottom spectrum, vertical $\widehat{A}$-cowaist and scalar curvature rigidity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917508006543360 |
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| author | Liu, Daoqiang |
| author_facet | Liu, Daoqiang |
| contents | We introduce the vertical \(\widehat{A}\)-cowaist, a codimension-one invariant for partitioned manifolds. It extends the concept of infinite vertical \(\widehat{A}\)-cowaist for bands to arbitrary partitioned manifolds, which may be noncompact and have compact boundary. We establish a sharp inequality relating the scalar curvature, the bottom spectrum of the Laplacian, and this invariant. As an application, we obtain a high-dimensional analogue of Munteanu-Wang's bottom spectrum estimate. We also prove a quantitative strengthening of Anghel's theorem together with a boundary version, as well as a Calabi-Yau type theorem that goes beyond the dimensional restrictions of the earlier \(μ\)-bubble method. Our approach is based on deformed Dirac operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bottom spectrum, vertical $\widehat{A}$-cowaist and scalar curvature rigidity Liu, Daoqiang Differential Geometry We introduce the vertical \(\widehat{A}\)-cowaist, a codimension-one invariant for partitioned manifolds. It extends the concept of infinite vertical \(\widehat{A}\)-cowaist for bands to arbitrary partitioned manifolds, which may be noncompact and have compact boundary. We establish a sharp inequality relating the scalar curvature, the bottom spectrum of the Laplacian, and this invariant. As an application, we obtain a high-dimensional analogue of Munteanu-Wang's bottom spectrum estimate. We also prove a quantitative strengthening of Anghel's theorem together with a boundary version, as well as a Calabi-Yau type theorem that goes beyond the dimensional restrictions of the earlier \(μ\)-bubble method. Our approach is based on deformed Dirac operators. |
| title | Bottom spectrum, vertical $\widehat{A}$-cowaist and scalar curvature rigidity |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.18269 |