Eternal Solutions to the Ricci Flow on $\R^2$
| dc.creator | Daskalopoulos, Panagiota | |
| dc.creator | Sesum, Natasa | |
| dc.date | 2006-03-22 | |
| dc.date | 2006-03-23 | |
| dc.date.accessioned | 2026-07-07T07:07:09Z | |
| dc.date.available | 2026-07-07T07:07:09Z | |
| dc.description | We provide the classification of eternal (or ancient) solutions of the two-dimensional Ricci flow, which is equivalent to the fast diffusion equation $ \frac{\partial u}{\partial t} = Δ\log u $ on $ \R^2 \times \R.$ We show that, under the necessary assumption that for every $t \in \R$, the solution $u(\cdot, t)$ defines a complete metric of bounded curvature and bounded width, $u$ is a gradient soliton of the form $ U(x,t) = \frac{2}{β(|x-x_0|^2 + δe^{2βt})}$, for some $x_0 \in \R^2$ and some constants $β>0$ and $δ>0$. | |
| dc.identifier | https://arxiv.org/abs/math/0603525 | |
| dc.identifier | http://arxiv.org/abs/math/0603525 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110286 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60 | |
| dc.title | Eternal Solutions to the Ricci Flow on $\R^2$ | |
| dc.type | text |