Non-singular solutions of normalized Ricci flow on noncompact manifolds of finite volume
| dc.creator | Fang, Fuquan | |
| dc.creator | Zhang, Yuguang | |
| dc.creator | Zhang, Zhenlei | |
| dc.date | 2008-11-25 | |
| dc.date.accessioned | 2026-07-07T10:36:30Z | |
| dc.date.available | 2026-07-07T10:36:30Z | |
| dc.description | The main result of this paper shows that, if $g(t)$ is a complete non-singular solution of the normalized Ricci flow on a noncompact 4-manifold $M$ of finite volume, then the Euler characteristic number $χ(M)\geq0$. Moreover, $χ(M)\neq 0$, there exist a sequence times $t_k\to\infty$, a double sequence of points $\{p_{k,l}\}_{l=1}^{N}$ and domains $\{U_{k,l}\}_{l=1}^{N}$ with $p_{k,l}\in U_{k,l}$ satisfying the followings: [(i)] $\dist_{g(t_k)}(p_{k,l_1},p_{k,l_2})\to\infty$ as $k\to\infty$, for any fixed $l_1\neq l_2$; [(ii)] for each $l$, $(U_{k,l},g(t_k),p_{k,l})$ converges in the $C_{loc}^\infty$ sense to a complete negative Einstein manifold $(M_{\infty,l},g_{\infty,l},p_{\infty,l})$ when $k\to\infty$; [(iii)] $\Vol_{g(t_{k})}(M\backslash\bigcup_{l=1}^{N}U_{k,l})\to0$ as $k\to\infty$. | |
| dc.identifier | https://arxiv.org/abs/0811.4028 | |
| dc.identifier | http://arxiv.org/abs/0811.4028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/180074 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.title | Non-singular solutions of normalized Ricci flow on noncompact manifolds of finite volume | |
| dc.type | text |