CAJ | 학술논문

设(Mn,g0)(n奇数)是紧Riemannian流形,λ(g0)>,这里λ(g0)是算子-4△g0+R(g0)的第一特征值,R(g0)是(Mn,g0)的数量曲率.设以(Mn,g0)为初值的规范化的Ricci流的极大解g(t)满足|R(g(t))|≤C和∫M|Rm((g(t))|n/2 dμt≤C (对某个常数C一致成立).我们证明这个解有子列收敛于一个Ricci收缩孤立子.进一步,当n=3时,条件∫M|Rm(g(t))|n/2 dμt≤C可去.
설(Mn,g0)(n기수)시긴Riemannian류형,λ(g0)>,저리λ(g0)시산자-4△g0+R(g0)적제일특정치,R(g0)시(Mn,g0)적수량곡솔.설이(Mn,g0)위초치적규범화적Ricci류적겁대해g(t)만족|R(g(t))|≤C화∫M|Rm((g(t))|n/2 dμt≤C (대모개상수C일치성립).아문증명저개해유자렬수렴우일개Ricci수축고립자.진일보,당n=3시,조건∫M|Rm(g(t))|n/2 dμt≤C가거.
Let (Mn,g0) with n odd be a compact Riemannian manifold with λ(g0)> 0,where λ(g0) is the first eigenvalue of the operator -4△g0 + R(g0),and R(g0) is the scalar curvature of (Mn,g0).Assume the maximal solution g(t) to the normalized Ricci flow with initial data (Mn,g0) satisfies |R(g(t))|≤ C and ∫M |Rm(g(t))|n/2dμt≤C uniformly for a constant C.Then we show that the solution sub-converges to a shrinking Ricci soliton.Moreover,when n=3,the condition ∫M|Rm(g(t))|n/2dμt≤C can be removed.