Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910878260002816 |
|---|---|
| author | Deruelle, Alix Schulze, Felix Simon, Miles |
| author_facet | Deruelle, Alix Schulze, Felix Simon, Miles |
| contents | This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from below and whose curvature is bounded by $c\cdot t^{-1}$ converge to one another at an exponential rate once they have been appropriately gauged. As an application, we show that smooth three dimensional, complete, uniformly Ricci-pinched Riemannian manifolds with bounded curvature are either compact or flat, thus confirming a conjecture of Hamilton and Lott. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_15313 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds Deruelle, Alix Schulze, Felix Simon, Miles Differential Geometry Analysis of PDEs This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from below and whose curvature is bounded by $c\cdot t^{-1}$ converge to one another at an exponential rate once they have been appropriately gauged. As an application, we show that smooth three dimensional, complete, uniformly Ricci-pinched Riemannian manifolds with bounded curvature are either compact or flat, thus confirming a conjecture of Hamilton and Lott. |
| title | Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2203.15313 |