On an invariant curvature cone along 4-dimensional Ricci flow
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909033476128768 |
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| author | Ding, Hongting Huang, Shaochuang Peng, Zhuo |
| author_facet | Ding, Hongting Huang, Shaochuang Peng, Zhuo |
| contents | In this paper, we study 4-dimensional complete non-compact manifold with its curvature operator in $\mathfrak{C}_{η,μ}$ via Ricci flow. We obtain topological and geometric gap theorems assuming such manifold has maximal volume growth. We also study 4-dimensional complete manifold with lower bound of $\mathfrak{C}_{η,μ}$ and obtain regularity results for Gromov-Hausdorff limit of complete volume non-collapsed manifolds with lower bound of $\mathfrak{C}_{η,μ}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10837 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On an invariant curvature cone along 4-dimensional Ricci flow Ding, Hongting Huang, Shaochuang Peng, Zhuo Differential Geometry 53E20 In this paper, we study 4-dimensional complete non-compact manifold with its curvature operator in $\mathfrak{C}_{η,μ}$ via Ricci flow. We obtain topological and geometric gap theorems assuming such manifold has maximal volume growth. We also study 4-dimensional complete manifold with lower bound of $\mathfrak{C}_{η,μ}$ and obtain regularity results for Gromov-Hausdorff limit of complete volume non-collapsed manifolds with lower bound of $\mathfrak{C}_{η,μ}$. |
| title | On an invariant curvature cone along 4-dimensional Ricci flow |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2605.10837 |