流在任意度量时刻的Immortal解

Immortal Solution of Ricci Flow at Any Metric Time

摘要:

通过解PoincaréLelong方程,完备非紧的n维的有着非负有界全纯双截曲率的Khler流形上的Ricci流方程被研究,如果它满足如下的条件:∫r0skt(x,s)ds≤qC log(2+r).那么Ricci流在任意度量时刻t存在Immortal解的充分必要条件被得到,它是对文献［1］在度量t=0时刻得到Ricci流存在Immortal解条件的推广.

关键词:PoincaréLelong方程; Ricci流; Immortal解; 有界曲率

Abstract:

The Ricci flow equation on n dimensional complete noncompact Khler manifolds is studied by solving the PoincaréLelong equation，if the following condition is satisfied:∫r0skt(x,s)ds≤qC log(2+r),then a necessary and sufficient condition for the existence of the immortal solution to the Ricci flow at any meric t time is obtained.It extends the result of Reference［1］that they get a necessary and sufficient condition for the existence of the immortal solution to the Ricci flow at metric t=0 time.

Key words:PoincaréLelong equation; Ricci flow; Immortal solution; bounded curvature