Ancient Ricci flows of bounded girth
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911697418059776 |
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| author | Bourni, Theodora Buttsworth, Timothy Lafuente, Ramiro Langford, Mat |
| author_facet | Bourni, Theodora Buttsworth, Timothy Lafuente, Ramiro Langford, Mat |
| contents | For each $n\ge 3$, we construct a 'pancake-like', $O(2)\times O(n-1)$-invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04964 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ancient Ricci flows of bounded girth Bourni, Theodora Buttsworth, Timothy Lafuente, Ramiro Langford, Mat Differential Geometry 53E20 For each $n\ge 3$, we construct a 'pancake-like', $O(2)\times O(n-1)$-invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle. |
| title | Ancient Ricci flows of bounded girth |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2302.04964 |