CAJ | 학술논문

设(M~3,g_0)是非紧三维Riemann流形,其Ricci曲率非负,单射半径有正的下界,且当x→∞时数量曲率R(x)→0.则以(M~3,g_0)为初始值的Ricci流在M~3×[0,∞)上有长期解.这推广了马和朱最近的一个结果,在高维情形我们也有相应的结果,并且我们给Chau,Tam和Yu在KhMer情形的类似定理一个新的证明.
설(M~3,g_0)시비긴삼유Riemann류형,기Ricci곡솔비부,단사반경유정적하계,차당x→∞시수량곡솔R(x)→0.칙이(M~3,g_0)위초시치적Ricci류재M~3×[0,∞)상유장기해.저추엄료마화주최근적일개결과,재고유정형아문야유상응적결과,병차아문급Chau,Tam화Yu재KhMer정형적유사정리일개신적증명.
Let (M~3,g_0) be a complete noucompaet Riemannian 3-mardfold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature R(x) → 0 as x→∞. Then the Ricci flow with initial data (M~3,g_0) has a long time solution on M~3 × [0, ∞). This extends a recent result of Ma and Zhu. We also have a higher dimensional version, and we reprove a KAhler analogue due to Chau, Tam and Yu.