Maximum principle and convergence of fundamental solutions for the Ricci flow
| dc.creator | Hsu, Shu-Yu | |
| dc.date | 2007-11-08 | |
| dc.date.accessioned | 2026-07-07T08:41:34Z | |
| dc.date.available | 2026-07-07T08:41:34Z | |
| dc.description | In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for the Ricci flow in $B_k\times (0,T)$ to the minimal fundamental solution of the conjugate heat equation as $k\to\infty$. We will prove the uniqueness of the fundamental solution under some exponential decay assumption on the fundamental solution. We will also give a detail proof of the convergence of the fundamental solutions of the conjugate heat equation for a sequence of pointed Ricci flow $(M_k\times (-α,0],x_k,g_k)$ to the fundamental solution of the limit manifold as $k\to\infty$ which was used without proof by Perelman in his proof of the pseudolocality theorem for Ricci flow. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0711.1236 | |
| dc.identifier | http://arxiv.org/abs/0711.1236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141711 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58J35, 53C43 | |
| dc.title | Maximum principle and convergence of fundamental solutions for the Ricci flow | |
| dc.type | text |