Ancient and expanding spin ALE Ricci flows
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917734349012992 |
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| author | Lopez, Isaac M. Ozuch, Tristan |
| author_facet | Lopez, Isaac M. Ozuch, Tristan |
| contents | We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in $SU(2)$ and mild decay at infinity are hyperkähler ALE metrics. The main idea of the proof, of independent interest, consists in showing that the large-scale behavior of Perelman's $μ$-functional on any ALE orbifold with non-negative scalar curvature is controlled by a renormalized $λ_{\mathrm{ALE}}$-functional related to a notion of weighted mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ancient and expanding spin ALE Ricci flows Lopez, Isaac M. Ozuch, Tristan Differential Geometry Mathematical Physics Analysis of PDEs We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in $SU(2)$ and mild decay at infinity are hyperkähler ALE metrics. The main idea of the proof, of independent interest, consists in showing that the large-scale behavior of Perelman's $μ$-functional on any ALE orbifold with non-negative scalar curvature is controlled by a renormalized $λ_{\mathrm{ALE}}$-functional related to a notion of weighted mass. |
| title | Ancient and expanding spin ALE Ricci flows |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2407.18438 |