The odd-dimensional long neck problem via spectral flow
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915471660417024 |
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| author | Shi, Pengshuai |
| author_facet | Shi, Pengshuai |
| contents | In this paper, we establish a scalar-mean curvature comparison theorem for the long neck problem on odd-dimensional spin manifolds. This extends previous work of Cecchini and Zeidler, and gives a complete answer to Gromov's long neck problem in terms of spin manifolds. As a related question, we prove a quantitative version of Llarull's theorem on non-compact spin manifolds. Our results are derived by studying the spectral flow of a family of Callias operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The odd-dimensional long neck problem via spectral flow Shi, Pengshuai Differential Geometry In this paper, we establish a scalar-mean curvature comparison theorem for the long neck problem on odd-dimensional spin manifolds. This extends previous work of Cecchini and Zeidler, and gives a complete answer to Gromov's long neck problem in terms of spin manifolds. As a related question, we prove a quantitative version of Llarull's theorem on non-compact spin manifolds. Our results are derived by studying the spectral flow of a family of Callias operators. |
| title | The odd-dimensional long neck problem via spectral flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.09809 |