No compact split limit Ricci flow of type II from the blow-down
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908343329619968 |
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| author | Zhao, Ziyi Zhu, Xiaohua |
| author_facet | Zhao, Ziyi Zhu, Xiaohua |
| contents | By Perelman's $\mathcal L$-geodesic theory, we study the blow-down solutions on a noncompact $κ$-noncollapsed steady gradient Ricci soliton $(M^n, g)$ $(n\ge 4)$ with nonnegative curvature operator and positive Ricci curvature away from a compact set of $M$. We prove that any compact split ancient solution of codimension one from the blow-down of $(M, g)$ is of type I. The result is a generalization of our previous work from $n=4$ to any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No compact split limit Ricci flow of type II from the blow-down Zhao, Ziyi Zhu, Xiaohua Differential Geometry Primary: 53E20, Secondary:53C20, 53C25, 58J05 By Perelman's $\mathcal L$-geodesic theory, we study the blow-down solutions on a noncompact $κ$-noncollapsed steady gradient Ricci soliton $(M^n, g)$ $(n\ge 4)$ with nonnegative curvature operator and positive Ricci curvature away from a compact set of $M$. We prove that any compact split ancient solution of codimension one from the blow-down of $(M, g)$ is of type I. The result is a generalization of our previous work from $n=4$ to any dimension. |
| title | No compact split limit Ricci flow of type II from the blow-down |
| topic | Differential Geometry Primary: 53E20, Secondary:53C20, 53C25, 58J05 |
| url | https://arxiv.org/abs/2404.18494 |