Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908593890000896 |
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| author | Chen, Jingche Hong, Han |
| author_facet | Chen, Jingche Hong, Han |
| contents | We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with boundary cannot have a metric of positive $m$-intermediate curvature if the boundary is $m$-convex, and some rigidity result holds if $m$-intermediate curvature is nonnegative. This non-existence persists after performing a connected sum with an arbitrary manifold. These results generalize results of \cite{brendle,chenshuli,ChuKwongLee,Xu} to manifold with boundary. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_13099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary Chen, Jingche Hong, Han Differential Geometry 53C23, 53C21 We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with boundary cannot have a metric of positive $m$-intermediate curvature if the boundary is $m$-convex, and some rigidity result holds if $m$-intermediate curvature is nonnegative. This non-existence persists after performing a connected sum with an arbitrary manifold. These results generalize results of \cite{brendle,chenshuli,ChuKwongLee,Xu} to manifold with boundary. |
| title | Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary |
| topic | Differential Geometry 53C23, 53C21 |
| url | https://arxiv.org/abs/2510.13099 |