Ancient Ricci flows with nonnegative Ricci curvature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917368562712576 |
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| author | Deng, Yuxing Wang, Ganqi Zhang, Yongjia |
| author_facet | Deng, Yuxing Wang, Ganqi Zhang, Yongjia |
| contents | In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity -- a noncollapsed $\mathbb{F}$-limit metric soliton [Bam23,CMZ23]. We first prove some estimates for noncollapsed $\mathbb{F}$-limit metric solitons with nonnegative Ricci curvature, and then obtain two dichotomy theorems for ancient Ricci flows. In particular, we show that: (1) for a noncollapsed ancient Ricci flow with nonnegative Ricci curvature, either its asymptotic volume ratio is always zero, or every tangent flow at infinity is a Ricci flat cone; (2) for a noncollapsed ancient Ricci flow with positively pinched Ricci curvature ($\operatorname{Ric}\ge \varepsilon R g$), either it is compact, or every tangent flow at infinity is a Ricci flat cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28014 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ancient Ricci flows with nonnegative Ricci curvature Deng, Yuxing Wang, Ganqi Zhang, Yongjia Differential Geometry In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity -- a noncollapsed $\mathbb{F}$-limit metric soliton [Bam23,CMZ23]. We first prove some estimates for noncollapsed $\mathbb{F}$-limit metric solitons with nonnegative Ricci curvature, and then obtain two dichotomy theorems for ancient Ricci flows. In particular, we show that: (1) for a noncollapsed ancient Ricci flow with nonnegative Ricci curvature, either its asymptotic volume ratio is always zero, or every tangent flow at infinity is a Ricci flat cone; (2) for a noncollapsed ancient Ricci flow with positively pinched Ricci curvature ($\operatorname{Ric}\ge \varepsilon R g$), either it is compact, or every tangent flow at infinity is a Ricci flat cone. |
| title | Ancient Ricci flows with nonnegative Ricci curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.28014 |