Ricci flow from singular spaces with bounded curvature
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915187556089856 |
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| author | Corro, Diego Zarei, Masoumeh Moreno, Adam |
| author_facet | Corro, Diego Zarei, Masoumeh Moreno, Adam |
| contents | We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow converges in the $C^{1,α}$-sense to a $C^{1,α}$-continuous Riemannian manifold which is isometric to the original metric space. Moreover, we prove that the flow is uniquely determined by the initial condition, up to isometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ricci flow from singular spaces with bounded curvature Corro, Diego Zarei, Masoumeh Moreno, Adam Differential Geometry Analysis of PDEs 53E20, 35K40, 53C20, 53C21, 53C23 We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow converges in the $C^{1,α}$-sense to a $C^{1,α}$-continuous Riemannian manifold which is isometric to the original metric space. Moreover, we prove that the flow is uniquely determined by the initial condition, up to isometry. |
| title | Ricci flow from singular spaces with bounded curvature |
| topic | Differential Geometry Analysis of PDEs 53E20, 35K40, 53C20, 53C21, 53C23 |
| url | https://arxiv.org/abs/2503.05896 |