L^2-instability of the Taub-Bolt metric under the Ricci flow
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916412671393792 |
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| author | Hughes, John |
| author_facet | Hughes, John |
| contents | In this paper we prove that there exists a compact perturbation of the Ricci flat Taub-Bolt metric that evolves under the Ricci flow into a finite time singularity modelled on the shrinking solition FIK [5]. Moreover, this perturbation can be made arbitrarily L^2-small with respect to the Taub-Bolt metric. The method of proof closely follows the strategy adopted in [14], where the author constructs, via a Ważewski box argument, Ricci flows on compact manifolds which encounter finite singularities modelled on a given asymptotically conical shrinking soliton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | L^2-instability of the Taub-Bolt metric under the Ricci flow Hughes, John Differential Geometry Analysis of PDEs In this paper we prove that there exists a compact perturbation of the Ricci flat Taub-Bolt metric that evolves under the Ricci flow into a finite time singularity modelled on the shrinking solition FIK [5]. Moreover, this perturbation can be made arbitrarily L^2-small with respect to the Taub-Bolt metric. The method of proof closely follows the strategy adopted in [14], where the author constructs, via a Ważewski box argument, Ricci flows on compact manifolds which encounter finite singularities modelled on a given asymptotically conical shrinking soliton. |
| title | L^2-instability of the Taub-Bolt metric under the Ricci flow |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2408.15269 |