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- W2950891496 abstract "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 $chi(M)geq0$. Moreover, $chi(M)neq 0$, there exist a sequence times $t_ktoinfty$, 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)] $dist_{g(t_k)}(p_{k,l_1},p_{k,l_2})toinfty$ as $ktoinfty$, for any fixed $l_1neq l_2$; [(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 $ktoinfty$; [(iii)] $Vol_{g(t_{k})}(Mbackslashbigcup_{l=1}^{N}U_{k,l})to0$ as $ktoinfty$." @default.
- W2950891496 created "2019-06-27" @default.
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- W2950891496 date "2008-11-25" @default.
- W2950891496 modified "2023-09-27" @default.
- W2950891496 title "Non-singular solutions of normalized Ricci flow on noncompact manifolds of finite volume" @default.
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