Inverse mean curvature flow and Ricci-pinched three-manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917708405145600 |
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| author | Huisken, Gerhard Koerber, Thomas |
| author_facet | Huisken, Gerhard Koerber, Thomas |
| contents | Let $(M,g)$ be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying $Ric\geq\varepsilon\,\operatorname{tr}(Ric)\,g$ for some $\varepsilon>0$. In this note, we give a new proof based on inverse mean curvature flow that $(M,g)$ is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04702 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverse mean curvature flow and Ricci-pinched three-manifolds Huisken, Gerhard Koerber, Thomas Differential Geometry Let $(M,g)$ be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying $Ric\geq\varepsilon\,\operatorname{tr}(Ric)\,g$ for some $\varepsilon>0$. In this note, we give a new proof based on inverse mean curvature flow that $(M,g)$ is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow. |
| title | Inverse mean curvature flow and Ricci-pinched three-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2305.04702 |