Asymptotic behavior of unstable perturbations of the Fubini-Study metric in Ricci flow
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909133738868736 |
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| author | Garfinkle, David Isenberg, James Knopf, Dan Wu, Haotian |
| author_facet | Garfinkle, David Isenberg, James Knopf, Dan Wu, Haotian |
| contents | Kröncke has shown that the Fubini-Study metric is an unstable generalized stationary solution of Ricci flow [Krö20]. In this paper, we carry out numerical simulations which indicate that Ricci flow solutions originating at unstable perturbations of the Fubini-Study metric develop local singularities modeled by the blowdown soliton discovered in [FIK03]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of unstable perturbations of the Fubini-Study metric in Ricci flow Garfinkle, David Isenberg, James Knopf, Dan Wu, Haotian Differential Geometry Numerical Analysis Analysis of PDEs Kröncke has shown that the Fubini-Study metric is an unstable generalized stationary solution of Ricci flow [Krö20]. In this paper, we carry out numerical simulations which indicate that Ricci flow solutions originating at unstable perturbations of the Fubini-Study metric develop local singularities modeled by the blowdown soliton discovered in [FIK03]. |
| title | Asymptotic behavior of unstable perturbations of the Fubini-Study metric in Ricci flow |
| topic | Differential Geometry Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2403.06427 |