Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929234499338240 |
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| author | Macbeth, Heather |
| author_facet | Macbeth, Heather |
| contents | We prove an $L^2$ estimate for the drift heat equation on a complete gradient shrinking Ricci soliton. This estimate has a time-dependent weight which is Gaussian in its spatial asymptotics. When transferred and scaled to an estimate for the heat equation along the Ricci flow of the soliton, this estimate is uniform up to the singular time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons Macbeth, Heather Differential Geometry 53C25, 53C44 We prove an $L^2$ estimate for the drift heat equation on a complete gradient shrinking Ricci soliton. This estimate has a time-dependent weight which is Gaussian in its spatial asymptotics. When transferred and scaled to an estimate for the heat equation along the Ricci flow of the soliton, this estimate is uniform up to the singular time. |
| title | Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons |
| topic | Differential Geometry 53C25, 53C44 |
| url | https://arxiv.org/abs/2402.03304 |