The Ricci flow on complete three-manifolds (Q2711941)

The authors consider the Ricci flow on three-dimensional complete noncompact Riemannian manifolds \((M^3,g)\) which satisfy the pointwise pinched condition \(R_c(X,Y)\geq \varepsilon Rg(X,Y)\), for some \(\varepsilon>0\), where \(R_c\) denotes the Ricci tensor and \(R\) the scalar curvature of \((M^3,g)\). Then they prove the existence of a solution \(g(x,t)\) for all times \(0\leq t<+\infty\) such that the curvature tensor \(R_m(x,t)\) of \(g(x,t)\) satisfies the following decay estimate \(|R_m(x,t) |\leq {C\over t}\), for \(x\in M^3\), \(t>0\), where \(C\) is some positive constant.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00021].